Entropy

Entropy, Vol. 14, Pages 233-251: Scientific Élan Vital: Entropy Deficit or Inhomogeneity as a Unified Concept of Driving Forces of Life in Hierarchical Biosphere Driven by Photosynthesis

Naoki Sato — Fri, 10 Feb 2012 00:00:00 CET

Life is considered something different from non-living things, but no single driving force can account for all the different aspects of life, which consists of different levels of hierarchy, such as metabolism, cell physiology, multi-cellular development and organization, population dynamics, ecosystem, and evolution. Although free energy is evidently the driving force in biochemical reactions, there is no established relationship between metabolic energy and spatiotemporal organization of living organisms, or between metabolic energy and genetic information. Since Schrödinger pointed out the importance of exporting entropy in maintaining life, misunderstandings of entropy notion have been obstacles in constructing a unified view on the driving forces of life. Here I present a simplified conceptual framework for unifying driving forces of life at various different levels of hierarchy. The key concept is “entropy deficit”, or simply, ‘inhomogeneity’, which is defined as the difference of maximal possible entropy and actual entropy. This is equivalent to information content in genetic information and protein structure, and is also defined similarly for non-homogeneous structures in ecosystems and evolution. Entropy deficit or inhomogeneoity is a unified measure of all driving forces of life, which could be considered a scientific equivalent to ‘élan vital’ of Bergson.

Entropy, Vol. 14, Pages 213-232: Quantitative Comparison of Conformational Ensembles

Kevin C. Wolfe — Fri, 10 Feb 2012 00:00:00 CET

A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to quantitatively compare two such ensembles is addressed in several different ways using concepts from probability and information theory. Ultimately, such metrics could be used in the evaluation of structure-prediction algorithms and the analysis of how conformational mobility is inhibited by bound ligands.

Entropy, Vol. 14, Pages 177-212: Disentangling Complexity from Randomness and Chaos

Lena C. Zuchowski — Tue, 07 Feb 2012 00:00:00 CET

This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively.

Entropy, Vol. 14, Pages 174-176: Special Issue: Tsallis Entropy

Anastasios Anastasiadis — Fri, 03 Feb 2012 00:00:00 CET

One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situation is not of this type and correlations may be far from negligible at all scales. Tsallis in 1988 introduced an entropic expression characterized by an index q which leads to a non-extensive statistics. Tsallis entropy, Sq, is the basis of the so called non-extensive statistical mechanics, which generalizes the Boltzmann-Gibbs theory. Tsallis statistics have found applications in a wide range of phenomena in diverse disciplines such as physics, chemistry, biology, medicine, economics, geophysics, etc. The focus of this special issue of Entropy was to solicit contributions that apply Tsallis entropy in various scientific fields. [...]

Entropy, Vol. 14, Pages 161-173: An Estimation of the Entropy for a Double Exponential Distribution Based on Multiply Type-II Censored Samples

Suk-Bok Kang — Tue, 31 Jan 2012 00:00:00 CET

In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Multiply Type-II censored sampling arises in a life-testing experiment whenever the experimenter does not observe the failure times of some units placed on a life-test. In this paper, we obtain estimators for the entropy function of a double exponential distribution under multiply Type-II censored samples using the maximum likelihood estimation and the approximate maximum likelihood estimation procedures. We compare the proposed estimators in the sense of the mean squared errors by using Monte Carlo simulation.

Entropy, Vol. 14, Pages 131-160: Control Parameters for Boundary-Layer Instabilities in Unsteady Shock Interactions

LaVar King Isaacson — Tue, 31 Jan 2012 00:00:00 CET

This article presents the computation of a set of control parameters for the deterministic prediction of laminar boundary-layer instabilities induced by an imposed unsteady shock interaction. The objective of the study is exploratory in nature by computing a supersonic flight environment for flow over a blunt body and the deterministic prediction of the spectral entropy rates for the boundary layer subjected to an unsteady pressure disturbance. The deterministic values for the spectral entropy rate within the instabilities are determined for each control parameter. Computational results imply that the instabilities are of a span-wise vortex form, that the maximum vertical velocity wave vector components are produced in the region nearest the wall and that extended transient coherent structures are produced in the boundary layer at a vertical location slightly below the mid-point of the boundary layer.

Entropy, Vol. 14, Pages 92-130: The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Gian Paolo Beretta — Mon, 30 Jan 2012 00:00:00 CET

The Rate-Controlled Constrained-Equilibrium (RCCE) method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.

Entropy, Vol. 14, Pages 74-91: A New Approach to Measure Volatility in Energy Markets

María del Carmen Ruiz — Mon, 23 Jan 2012 00:00:00 CET

Several measures of volatility have been developed in order to quantify the degree of uncertainty of an energy price series, which include historical volatility and price velocities, among others. This paper suggests using the permutation entropy, topological entropy and the modified permutation entropy as alternatives to measure volatility in energy markets. Simulated data show that these measures are more appropriate to quantify the uncertainty associated to a time series than those based on the standard deviation or other measures of dispersion. Finally, the proposed method is applied to some typical electricity markets: Nord Pool, Ontario, Omel and four Australian markets.

Entropy, Vol. 14, Pages 58-73: Thermodynamic Modeling for Open Combined Regenerative Brayton and Inverse Brayton Cycles with Regeneration before the Inverse Cycle

Lingen Chen — Tue, 10 Jan 2012 00:00:00 CET

A thermodynamic model of an open combined regenerative Brayton and inverse Brayton cycles with regeneration before the inverse cycle is established in this paper by using thermodynamic optimization theory. The flow processes of the working fluid with the pressure drops and the size constraint of the real power plant are modeled. There are 13 flow resistances encountered by the working fluid stream for the cycle model. Four of these, the friction through the blades and vanes of the compressors and the turbines, are related to the isentropic efficiencies. The remaining nine flow resistances are always present because of the changes in flow cross-section at the compressor inlet of the top cycle, regenerator inlet and outlet, combustion chamber inlet and outlet, turbine outlet of the top cycle, turbine outlet of the bottom cycle, heat exchanger inlet, and compressor inlet of the bottom cycle. These resistances associated with the flow through various cross-sectional areas are derived as functions of the compressor inlet relative pressure drop of the top cycle, and control the air flow rate, the net power output and the thermal efficiency. The analytical formulae about the power output, efficiency and other coefficients are derived with 13 pressure drop losses. It is found that the combined cycle with regenerator can reach higher thermal efficiency but smaller power output than those of the base combined cycle at small compressor inlet relative pressure drop of the top cycle.

Entropy, Vol. 14, Pages 32-57: Statistical Dynamical Closures and Subgrid Modeling for Inhomogeneous QG and 3D Turbulence

Jorgen S. Frederiksen — Wed, 04 Jan 2012 00:00:00 CET

Statistical dynamical closures for inhomogeneous turbulence described by multi‑field equations are derived based on renormalized perturbation theory. Generalizations of the computationally tractable quasi-diagonal direct interaction approximation for inhomogeneous barotropic turbulent flows over topography are developed. Statistical closures are also formulated for large eddy simulations including subgrid models that ensure the same large scale statistical behavior as higher resolution closures. The focus is on baroclinic quasigeostrophic and three-dimensional inhomogeneous turbulence although the framework is generally applicable to classical field theories with quadratic nonlinearity.

Entropy, Vol. 14, Pages 24-31: On the Role of Entropy Generation in Processes Involving Fatigue

Mehdi Amiri — Fri, 30 Dec 2011 00:00:00 CET

In this paper we describe the potential of employing the concept of thermodynamic entropy generation to assess degradation in processes involving metal fatigue. It is shown that empirical fatigue models such as Miner’s rule, Coffin-Manson equation, and Paris law can be deduced from thermodynamic consideration.

Entropy, Vol. 14, Pages 1-23: Entropy Generation Analysis of Open Parallel Microchannels Embedded Within a Permeable Continuous Moving Surface: Application to Magnetohydrodynamics (MHD)

Mohammad H. Yazdi — Tue, 27 Dec 2011 00:00:00 CET

This paper presents a new design of open parallel microchannels embedded within a permeable continuous moving surface due to reduction of exergy losses in magnetohydrodynamic (MHD) flow at a prescribed surface temperature (PST). The entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by an explicit Runge-Kutta (4, 5) formula, the Dormand-Prince pair and shooting method. The entropy generation number, as well as the Bejan number, for various values of the involved parameters of the problem are also presented and discussed in detail.

Entropy, Vol. 13, Pages 2049-2058: Information Theory Consequences of the Scale-Invariance of Schröedinger’s Equation

Silvana Flego — Tue, 20 Dec 2011 00:00:00 CET

In this communication we show that Fisher’s information measure emerges as a direct consequence of the scale-invariance of Schröedinger’s equation. Interesting, well-known additional results are re-obtained as well, for whose derivation only (and this is the novelty) the scale invariance property is needed, without further ado.

Entropy, Vol. 13, Pages 2036-2048: Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy

Shih-Feng Shieh — Tue, 20 Dec 2011 00:00:00 CET

The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues of A and A + V.

Entropy, Vol. 13, Pages 2024-2035: Fluctuation, Dissipation and the Arrow of Time

Michele Campisi — Mon, 19 Dec 2011 00:00:00 CET

The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question.

Entropy, Vol. 13, Pages 2013-2023: Coincidences and Estimation of Entropies of Random Variables with Large Cardinalities

Ilya Nemenman — Mon, 19 Dec 2011 00:00:00 CET

We perform an asymptotic analysis of the NSB estimator of entropy of a discrete random variable. The analysis illuminates the dependence of the estimates on the number of coincidences in the sample and shows that the estimator has a well defined limit for a large cardinality of the studied variable. This allows estimation of entropy with no a priori assumptions about the cardinality. Software implementation of the algorithm is available.

Entropy, Vol. 13, Pages 1992-2012: Effects of Radiation Heat Transfer on Entropy Generation at Thermosolutal Convection in a Square Cavity Subjected to a Magnetic Field

Nejib Hidouri — Mon, 28 Nov 2011 00:00:00 CET

Thermosolutal convection in a square cavity filled with a binary perfect gas mixture and submitted to an oriented magnetic field taking into account the effect of radiation heat transfer is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined for laminar flow by solving numerically: The continuity, momentum energy and mass balance equations, using a Control Volume Finite-Element Method. The structure of the studied flows depends on five dimensionless parameters which are: The Grashof number, the buoyancy ratio, the Hartman number, the inclination angle of the magnetic field and the radiation parameter.

Entropy, Vol. 13, Pages 1967-1991: Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

Irina Dymnikova — Mon, 28 Nov 2011 00:00:00 CET

We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGTμν = Λδμν as r → 0, 8πGTμν = λδμν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter Mcr1 ≤ M ≤ Mcr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon rb < rc, and an internal horizon ra < rb, which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basicfeatures of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q =√Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon rb and cosmological horizon rc. We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (ra = rb) remnant with the positive specific heat and zero temperature.

Entropy, Vol. 13, Pages 1958-1966: Loop Entropy Assists Tertiary Order: Loopy Stabilization of Stacking Motifs

Daniel P. Aalberts — Thu, 24 Nov 2011 00:00:00 CET

The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of forming multibranch and other RNA loops is derived with a polymer-physics based theory. We also derive a formula for the free energy of coaxial stacking in the context of a loop. Simulations support the analytic formulas. The effects of stacking of unpaired bases are also studied with simulations.

Entropy, Vol. 13, Pages 1945-1957: A Characterization of Entropy in Terms of Information Loss

John C. Baez — Thu, 24 Nov 2011 00:00:00 CET

There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the “information loss”, or change in entropy, associated with a measure-preserving function. Information loss is a special case of conditional entropy: namely, it is the entropy of a random variable conditioned on some function of that variable. We show that Shannon entropy gives the only concept of information loss that is functorial, convex-linear and continuous. This characterization naturally generalizes to Tsallis entropy as well.

Entropy, Vol. 13, Pages 1928-1944: Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy

Mauricio S. Ribeiro — Tue, 01 Nov 2011 00:00:00 CET

Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional Fokker-Planck equation is derived directly from a master equation, by considering nonlinearitiesin the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved;for that, an important relation involving these equations and general entropic forms is introduced. It is shown that due to this relation, classes of nonlinear N-dimensional Fokker-Planck equations are connected to a single entropic form. A particular emphasis is given to the class of equations associated to Tsallis entropy, in both cases of the standard, and generalized definitions for the internal energy.

Entropy, Vol. 13, Pages 1916-1927: A Generalized Maximum Entropy Stochastic Frontier Measuring Productivity Accounting for Spatial Dependency

Axel Tonini — Fri, 28 Oct 2011 00:00:00 CEST

In this paper, a stochastic frontier model accounting for spatial dependency is developed using generalized maximum entropy estimation. An application is made for measuring total factor productivity in European agriculture. The empirical results show that agricultural productivity growth in Europe is driven by upward movements of technology over time through technological developments. Results are then compared for a situation in which spatial dependency in the technical inefficiency effects is not accounted.

Entropy, Vol. 13, Pages 1904-1915: Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics

Kuang-Dai Leng — Wed, 26 Oct 2011 00:00:00 CEST

Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative external forces. Yet this general result holds true even without the Green-inelasticity presumption under a more general interpretation of the infinitesimal internal rearrangement. Three special cases are discussed following the generalized form: (a) the Green-elastic bodies whose free energy can be identified with the strain energy; (b) the Green-inelastic bodies composed of materials compliant with the additive decomposition of strain; and (c) the Green-inelastic bodies undergoing isothermal relaxation processes where the thermodynamic forces conjugate to internal variables, or the so-termed internal forces prove to be potential forces. This paper can be viewed as an extension of Yang et al. [1].

Entropy, Vol. 13, Pages 1882-1903: On the Growth Rate of Non-Enzymatic Molecular Replicators

Harold Fellermann — Fri, 21 Oct 2011 00:00:00 CEST

It is well known that non-enzymatic template directed molecular replicators X + nO -> 2X exhibit parabolic growth d[X]/dt -> k[X]1/2. Here, we analyze the dependence of the effective replication rate constant k on hybridization energies, temperature, strand length, and sequence composition. First we derive analytical criteria for the replication rate k based on simple thermodynamic arguments. Second we present a Brownian dynamics model for oligonucleotides that allows us to simulate their diffusion and hybridization behavior. The simulation is used to generate and analyze the effect of strand length, temperature, and to some extent sequence composition, on the hybridization rates and the resulting optimal overall rate constant k. Combining the two approaches allows us to semi-analytically depict a replication rate landscape for template directed replicators. The results indicate a clear replication advantage for longer strands at lower temperatures in the regime where the ligation rate is rate limiting. Further the results indicate the existence of an optimal replication rate at the boundary between the two regimes where the ligation rate and the dehybridization rates are rate limiting.

Entropy, Vol. 13, Pages 1865-1881: Quantifying Dynamical Complexity of Magnetic Storms and Solar Flares via Nonextensive Tsallis Entropy

Georgios Balasis — Fri, 14 Oct 2011 00:00:00 CEST

Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe attempts to approach the dynamics of magnetic storms and solar flares by means of universality through Tsallis statistics. We also include a discussion of possible implications on space weather forecasting efforts arising from the verification of Tsallis entropy in the complex system of the magnetosphere.

Entropy, Vol. 13, Pages 1829-1864: Entropy Generation Analysis of Desalination Technologies

Karan H. Mistry — Fri, 30 Sep 2011 00:00:00 CEST

Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.

Entropy, Vol. 13, Pages 1805-1828: Tsallis Entropy for Geometry Simplification

Pascual Castelló — Thu, 29 Sep 2011 00:00:00 CEST

This paper presents a study and a comparison of the use of different information-theoretic measures for polygonal mesh simplification. Generalized measures from Information Theory such as Havrda–Charvát–Tsallis entropy and mutual information have been applied. These measures have been used in the error metric of a surfaces implification algorithm. We demonstrate that these measures are useful for simplifying three-dimensional polygonal meshes. We have also compared these metrics with the error metrics used in a geometry-based method and in an image-driven method. Quantitative results are presented in the comparison using the root-mean-square error (RMSE).

Entropy, Vol. 13, Pages 1765-1804: The Nonadditive Entropy Sq and Its Applications in Physics and Elsewhere: Some Remarks

Constantino Tsallis — Wed, 28 Sep 2011 00:00:00 CEST

The nonadditive entropy Sq has been introduced in 1988 focusing on a generalization of Boltzmann–Gibbs (BG) statistical mechanics. The aim was to cover a (possibly wide) class of systems among those very many which violate hypothesis such as ergodicity, under which the BG theory is expected to be valid. It is now known that Sq has a large applicability; more specifically speaking, even outside Hamiltonian systems and their thermodynamical approach. In the present paper we review and comment some relevant aspects of this entropy, namely (i) Additivity versus extensivity; (ii) Probability distributions that constitute attractors in the sense of Central Limit Theorems; (iii) The analysis of paradigmatic low-dimensional nonlinear dynamical systems near the edge of chaos; and (iv) The analysis of paradigmatic long-range-interacting many-body classical Hamiltonian systems. Finally, we exhibit recent as well as typical predictions, verifications and applications of these concepts in natural, artificial, and social systems, as shown through theoretical, experimental, observational and computational results.

Entropy, Vol. 13, Pages 1746-1764: Projective Power Entropy and Maximum Tsallis Entropy Distributions

Shinto Eguchi — Mon, 26 Sep 2011 00:00:00 CEST

We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterization problem of which conditions uniquely determine the projective power entropy up to the power index. A close relation of the entropy with the Lebesgue space Lp and the dual Lq is explored, in which the escort distribution associates with an interesting property. When we consider maximum Tsallis entropy distributions under the constraints of the mean vector and variance matrix, the model becomes a multivariate q-Gaussian model with elliptical contours, including a Gaussian and t-distribution model. We discuss the statistical estimation by minimization of the empirical loss associated with the projective power entropy. It is shown that the minimum loss estimator for the mean vector and variance matrix under the maximum entropy model are the sample mean vector and the sample variance matrix. The escort distribution of the maximum entropy distribution plays the key role for the derivation.

Entropy, Vol. 13, Pages 1730-1745: Blind Deconvolution of Seismic Data Using f-Divergences

Bing Zhang — Mon, 19 Sep 2011 00:00:00 CEST

This paper proposes a new approach to the seismic blind deconvolution problem in the case of band-limited seismic data characterized by low dominant frequency and short data records, based on Csiszár’s f-divergence. In order to model the probability density function of the deconvolved data, and obtain the closed form formula of Csiszár’s f-divergence, mixture Jones’ family of distributions (MJ) is introduced, by which a new criterion for blind deconvolution is constructed. By applying Neidell’s wavelet model to the inverse filter, we then make the optimization program for multivariate reduce to univariate case. Examples are provided showing the good performance of the method, even in low SNR situations.

Entropy, Vol. 13, Pages 1708-1729: An Artificial Bee Colony Algorithm for the Job Shop Scheduling Problem with Random Processing Times

Rui Zhang — Mon, 19 Sep 2011 00:00:00 CEST

Due to the influence of unpredictable random events, the processing time of each operation should be treated as random variables if we aim at a robust production schedule. However, compared with the extensive research on the deterministic model, the stochastic job shop scheduling problem (SJSSP) has not received sufficient attention. In this paper, we propose an artificial bee colony (ABC) algorithm for SJSSP with the objective of minimizing the maximum lateness (which is an index of service quality). First, we propose a performance estimate for preliminary screening of the candidate solutions. Then, the K-armed bandit model is utilized for reducing the computational burden in the exact evaluation (through Monte Carlo simulation) process. Finally, the computational results on different-scale test problems validate the effectiveness and efficiency of the proposed approach.

Entropy, Vol. 13, Pages 1694-1707: Tsallis Mutual Information for Document Classification

Màrius Vila — Wed, 14 Sep 2011 00:00:00 CEST

Mutual information is one of the mostly used measures for evaluating image similarity. In this paper, we investigate the application of three different Tsallis-based generalizations of mutual information to analyze the similarity between scanned documents. These three generalizations derive from the Kullback–Leibler distance, the difference between entropy and conditional entropy, and the Jensen–Tsallis divergence, respectively. In addition, the ratio between these measures and the Tsallis joint entropy is analyzed. The performance of all these measures is studied for different entropic indexes in the context of document classification and registration.

Entropy, Vol. 13, Pages 1664-1693: Relativistic Statistical Mechanics vs. Relativistic Thermodynamics

Gonzalo Ares de Parga — Fri, 09 Sep 2011 00:00:00 CEST

Based on a covariant theory of equilibrium Thermodynamics, a Statistical Relativistic Mechanics is developed for the non-interacting case. Relativistic Thermodynamics and Jüttner Relativistic Distribution Function in a moving frame are obtained by using this covariant theory. A proposal for a Relativistic Statistical Mechanics is exposed for the interacting case.

Entropy, Vol. 13, Pages 1648-1663: Wavelet Fisher’s Information Measure of 1=f α Signals

Julio Ramírez-Pacheco — Tue, 06 Sep 2011 00:00:00 CEST

This article defines the concept of wavelet-based Fisher’s information measure (wavelet FIM) and develops a closed-form expression of this measure for 1=f α signals. Wavelet Fisher’s information measure characterizes the complexities associated to 1=f α signals and provides a powerful tool for their analysis. Theoretical and experimental studies demonstrate that this quantity is exponentially increasing for α > 1 (non-stationary signals) and almost constant for α < 1 (stationary signals). Potential applications of wavelet FIM are discussed in some detail and its power and robustness for the detection of structural breaks in the mean embedded in stationary fractional Gaussian noise signals studied.

Entropy, Vol. 13, Pages 1611-1647: Universal Property of Quantum Gravity implied by Uniqueness Theorem of Bekenstein-Hawking Entropy

Hiromi Saida — Mon, 05 Sep 2011 00:00:00 CEST

This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the second part, intrinsic properties of quantum mechanics are shown, which justify the Boltzmann formula to yield a unique entropy in statistical mechanics. These properties clarify three conditions, one of which is necessary and others are sufficient for the validity of Boltzmann formula. In the third part, by combining the above results, we find a reasonable suggestion from the sufficient conditions that the potential of gravitational interaction among microstates of underlying quantum gravity may not diverge to negative infinity (such as Newtonian gravity) but is bounded below at a finite length scale. In addition to that, from the necessary condition, the interaction has to be repulsive within the finite length scale. The length scale should be Planck size. Thus, quantum gravity may become repulsive at Planck length. Also, a relation of these suggestions with action integral of gravity at semi-classical level is given. These suggestions about quantum gravity are universal in the sense that they are independent of any existing model of quantum gravity.

Entropy, Vol. 13, Pages 1595-1610: The Effect of Thermal Radiation on Entropy Generation Due to Micro-Polar Fluid Flow Along a Wavy Surface

Cha’o-Kuang Chen — Fri, 02 Sep 2011 00:00:00 CEST

In this study, the effect of thermal radiation on micro-polar fluid flow over a wavy surface is studied. The optically thick limit approximation for the radiation flux is assumed. Prandtl’s transposition theorem is used to stretch the ordinary coordinate system in certain directions. The wavy surface can be transferred into a calculable plane coordinate system. The governing equations of micro-polar fluid along a wavy surface are derived from the complete Navier-Stokes equations. A simple transformation is proposed to transform the governing equations into boundary layer equations so they can be solved numerically by the cubic spline collocation method. A modified form for the entropy generation equation is derived. Effects of thermal radiation on the temperature and the vortex viscosity parameter and the effects of the wavy surface on the velocity are all included in the modified entropy generation equation.

Entropy, Vol. 13, Pages 1584-1594: Local Stability Analysis of a Thermo-Economic Model of a Chambadal-Novikov-Curzon-Ahlborn Heat Engine

Marco A. Barranco-Jiménez — Mon, 29 Aug 2011 00:00:00 CEST

In this work we present a local stability analysis of the thermo-economic model of an irreversible heat engine working at maximum power conditions. The thermo-economic model is based on the maximization of a benefit function which is defined by the ratio of the power output and the total cost involved in the plant’s performance. Our study shows that, after a small perturbation, the system decays exponentially to the steady state determined by two different relaxation times. In particular, we show that the relaxation times are function of the temperature ratio τ = T2/T1 (T1 > T2), the cost function ƒ and the parameter R (a parameter related to the degree of internal irreversibilities). We observe that the stability of the system improves as τ increases whereas for changes in ƒ and R, the stability properties are characterized by a rapid decay along the fast eigendirection as ƒ increases and R decreases. Finally, we discuss our results in the context of energetic properties.

Entropy, Vol. 13, Pages 1555-1583: Spectral Entropy in a Boundary-Layer Flow

LaVar King Isaacson — Fri, 26 Aug 2011 00:00:00 CEST

This article presents a comparison of the entropy production in a laminar and transitional boundary layer flow with the spectral entropy produced in a region of instability induced by an imposed periodic disturbance. The objective of the study is exploratory in nature by computing a boundary-layer environment with well-established computer techniques and comparing the predictions of the maximum rate of entropy production in the wall shear layer with the deterministic prediction of the spectral entropy growth within an inceptive instability in the inner region of the upstream boundary-layer flow. The deterministic values of the spectral entropy within the instability are brought into agreement with the computed rate of entropy production inversely along the shear flow with the assumption that the instability is of a span-wise vortex form and that the spectral entropy components are transported into the wall shear layer by vortex down sweep and are processed into thermodynamic entropy in the boundary-layer wall region.

Entropy, Vol. 13, Pages 1541-1554: Phase-Controlled Atom-Photon Entanglement in a Three-Level V-Type Atomic System via Spontaneously Generated Coherence

Mohammad Abazari — Thu, 25 Aug 2011 00:00:00 CEST

We investigate the dynamical behavior of the atom-photon entanglement in a V-type three-level quantum system using the atomic reduced entropy. It is shown that an atom and photons are entangled at the steady-state; however disentanglement can also be achieved in an special condition. It is demonstrated that in the presence of quantum interference induced by spontaneous emission, the reduced entropy and the atom-photon entanglement are phase-dependent. A non-stationary solution is also obtained when the quantum interference due to the spontaneous emission is completely included.

Entropy, Vol. 13, Pages 1533-1540: Distinguishability in Entropy Calculations: Chemical Reactions, Conformational and Residual Entropy

Ernesto Suárez — Tue, 23 Aug 2011 00:00:00 CEST

By analyzing different examples of practical entropy calculations and using concepts such as conformational and residual entropies, I show herein that experimental calorimetric entropies of single molecules can be theoretically reproduced considering chemically identical atoms either as distinguishable or indistinguishable particles. The broadly used correction in entropy calculations due to the symmetry number and particle indistinguishability is not mandatory, as an ad hoc correction, to obtain accurate values of absolute and relative entropies. It is shown that, for any chemical reaction of any kind, considering distinguishability or indistinguishability among identical atoms is irrelevant as long as we act consistently in the calculation of all the required entropy contributions.

Entropy, Vol. 13, Pages 1518-1532: A Risk Profile for Information Fusion Algorithms

Kenric P. Nelson — Wed, 17 Aug 2011 00:00:00 CEST

E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is because robustness requires discarding of information in order to reduce the sensitivity to outliers. The principal of nonlinear statistical coupling, which is an interpretation of the Tsallis entropy generalization, can be used to quantify this trade-off. The coupled-surprisal, -lnκ(p)≡-(pκ-1)/κ , is a generalization of Shannon surprisal or the logarithmic scoring rule, given a forecast p of a true event by an inferencing algorithm. The coupling parameter κ=1-q, where q is the Tsallis entropy index, is the degree of nonlinear coupling between statistical states. Positive (negative) values of nonlinear coupling decrease (increase) the surprisal information metric and thereby biases the risk in favor of decisive (robust) algorithms relative to the Shannon surprisal (κ=0). We show that translating the average coupled-surprisal to an effective probability is equivalent to using the generalized mean of the true event probabilities as a scoring rule. The metric is used to assess the robustness, accuracy, and decisiveness of a fusion algorithm. We use a two-parameter fusion algorithm to combine input probabilities from N sources. The generalized mean parameter ‘alpha’ varies the degree of smoothing and raising to a power Νβ with β between 0 and 1 provides a model of correlation.

Entropy, Vol. 13, Pages 1481-1517: Thermodynamics of Thermoelectric Phenomena and Applications

Christophe Goupil — Mon, 15 Aug 2011 00:00:00 CEST

Fifty years ago, the optimization of thermoelectric devices was analyzed by considering the relation between optimal performances and local entropy production. Entropy is produced by the irreversible processes in thermoelectric devices. If these processes could be eliminated, entropy production would be reduced to zero, and the limiting Carnot efficiency or coefficient of performance would be obtained. In the present review, we start with some fundamental thermodynamic considerations relevant for thermoelectrics. Based on a historical overview, we reconsider the interrelation between optimal performances and local entropy production by using the compatibility approach together with the thermodynamic arguments. Using the relative current density and the thermoelectric potential, we show that minimum entropy production can be obtained when the thermoelectric potential is a specific, optimal value.

Entropy, Vol. 13, Pages 1465-1480: Size of the Whole versus Number of Parts in Genomes

Antoni Hernández-Fernández — Fri, 05 Aug 2011 00:00:00 CEST

It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind “the more parts the smaller the whole” as in angiosperms, but also relationships of the kind “the more parts the larger the whole”. Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent.

Entropy, Vol. 13, Pages 1446-1464: Second Law Analysis for Variable Viscosity Hydromagnetic Boundary Layer Flow with Thermal Radiation and Newtonian Heating

Oluwole Daniel Makinde — Fri, 05 Aug 2011 00:00:00 CEST

The present paper is concerned with the analysis of inherent irreversibility in hydromagnetic boundary layer flow of variable viscosity fluid over a semi-infinite flat plate under the influence of thermal radiation and Newtonian heating. Using local similarity solution technique and shooting quadrature, the velocity and temperature profiles are obtained numerically and utilized to compute the entropy generation number. The effects of magnetic field parameter, Brinkmann number, the Prandtl number, variable viscosity parameter, radiation parameter and local Biot number on the fluid velocity profiles, temperature profiles, local skin friction and local Nusselt number are presented. The influences of the same parameters and the dimensionless group parameter on the entropy generation rate in the flow regime and Bejan number are calculated, depicted graphically and discussed quantitatively. It is observed that the peak of entropy generation rate is attained within the boundary layer region and plate surface act as a strong source of entropy generation and heat transfer irreversibility.

Entropy, Vol. 13, Pages 1425-1445: A Maximum Entropy Estimator for the Aggregate Hierarchical Logit Model

Pedro Donoso — Tue, 02 Aug 2011 00:00:00 CEST

A new approach for estimating the aggregate hierarchical logit model is presented. Though usually derived from random utility theory assuming correlated stochastic errors, the model can also be derived as a solution to a maximum entropy problem. Under the latter approach, the Lagrange multipliers of the optimization problem can be understood as parameter estimators of the model. Based on theoretical analysis and Monte Carlo simulations of a transportation demand model, it is demonstrated that the maximum entropy estimators have statistical properties that are superior to classical maximum likelihood estimators, particularly for small or medium-size samples. The simulations also generated reduced bias in the estimates of the subjective value of time and consumer surplus.

Entropy, Vol. 13, Pages 1403-1424: Joint Markov Blankets in Feature Sets Extracted from Wavelet Packet Decompositions

Gert Van Dijck — Fri, 22 Jul 2011 00:00:00 CEST

Since two decades, wavelet packet decompositions have been shown effective as a generic approach to feature extraction from time series and images for the prediction of a target variable. Redundancies exist between the wavelet coefficients and between the energy features that are derived from the wavelet coefficients. We assess these redundancies in wavelet packet decompositions by means of the Markov blanket filtering theory. We introduce the concept of joint Markov blankets. It is shown that joint Markov blankets are a natural extension of Markov blankets, which are defined for single features, to a set of features. We show that these joint Markov blankets exist in feature sets consisting of the wavelet coefficients. Furthermore, we prove that wavelet energy features from the highest frequency resolution level form a joint Markov blanket for all other wavelet energy features. The joint Markov blanket theory indicates that one can expect an increase of classification accuracy with the increase of the frequency resolution level of the energy features.

Entropy, Vol. 13, Pages 1380-1402: Diffuser and Nozzle Design Optimization by Entropy Generation Minimization

Bastian Schmandt — Wed, 20 Jul 2011 00:00:00 CEST

Diffusers and nozzles within a flow system are optimized with respect to their wall shapes for a given change in cross sections. The optimization target is a low value of the head loss coefficient K, which can be linked to the overall entropy generation due to the conduit component. First, a polynomial shape of the wall with two degrees of freedom is assumed. As a second approach six equally spaced diameters in a diffuser are determined by a genetic algorithm such that the entropy generation and thus the head loss is minimized. It turns out that a visualization of cross section averaged entropy generation rates along the flow path should be used to identify sources of high entropy generation before and during the optimization. Thus it will be possible to decide whether a given parametric representation of a component’s shape only leads to a redistribution of losses or (in the most-favored case) to minimal values for K.

Entropy, Vol. 13, Pages 1355-1379: Effective Conformal Descriptions of Black Hole Entropy

Steven Carlip — Wed, 20 Jul 2011 00:00:00 CEST

It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective “conformal dual” description that is largely independent of the microscopic details.

Entropy, Vol. 13, Pages 1324-1354: Partition Function of the Schwarzschild Black Hole

Jarmo Mäkelä — Tue, 19 Jul 2011 00:00:00 CEST

We consider a microscopic model of a stretched horizon of the Schwarzschild black hole. In our model the stretched horizon consists of a finite number of discrete constituents. Assuming that the quantum states of the Schwarzschild black hole are encoded in the quantum states of the constituents of its stretched horizon in a certain manner we obtain an explicit, analytic expression for the partition function of the hole. Our partition function predicts, among other things, the Hawking effect, and provides it with a microscopic, statistical interpretation.

Entropy, Vol. 13, Pages 1305-1323: State Operator Correspondence and Entanglement in AdS2/CFT1

Ashoke Sen — Tue, 19 Jul 2011 00:00:00 CEST

Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are described by the twisted version of the Hartle–Hawking states, the twists being generated by a large unitary group of symmetries that this string theory must possess. This formalism makes natural the dual interpretation of the black hole entropy—as the logarithm of the degeneracy of ground states of the quantum mechanics describing the low energy dynamics of the black hole, and also as an entanglement entropy between the two copies of the same quantum theory living on the two boundaries of global AdS2 separated by the event horizon.

Entropy, Vol. 13, Pages 1281-1304: Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches

Michael J. Markham — Mon, 18 Jul 2011 00:00:00 CEST

Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian) network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME) are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.

Entropy, Vol. 13, Pages 1267-1280: Tsallis-Based Nonextensive Analysis of the Southern California Seismicity

Luciano Telesca — Mon, 11 Jul 2011 00:00:00 CEST

Nonextensive statistics has been becoming a very useful tool to describe the complexity of dynamic systems. Recently, analysis of the magnitude distribution of earthquakes has been increasingly used in the context of nonextensivity. In the present paper, the nonextensive analysis of the southern California earthquake catalog was performed. The results show that the nonextensivity parameter q lies in the same range as obtained for other different seismic areas, thus suggesting a sort of universal character in the nonextensive interpretation of seismicity.

Entropy, Vol. 13, Pages 1229-1266: On Accuracy of PDF Divergence Estimators and Their Applicability to Representative Data Sampling

Marcin Budka — Fri, 08 Jul 2011 00:00:00 CEST

Generalisation error estimation is an important issue in machine learning. Cross-validation traditionally used for this purpose requires building multiple models and repeating the whole procedure many times in order to produce reliable error estimates. It is however possible to accurately estimate the error using only a single model, if the training and test data are chosen appropriately. This paper investigates the possibility of using various probability density function divergence measures for the purpose of representative data sampling. As it turned out, the first difficulty one needs to deal with is estimation of the divergence itself. In contrast to other publications on this subject, the experimental results provided in this study show that in many cases it is not possible unless samples consisting of thousands of instances are used. Exhaustive experiments on the divergence guided representative data sampling have been performed using 26 publicly available benchmark datasets and 70 PDF divergence estimators, and their results have been analysed and discussed.

Entropy, Vol. 13, Pages 1212-1228: Application of the EGM Method to a LED-Based Spotlight: A Constrained Pseudo-Optimization Design Process Based on the Analysis of the Local Entropy Generation Maps

Giorgio Giangaspero — Mon, 27 Jun 2011 00:00:00 CEST

In this paper, the entropy generation minimization (EGM) method is applied to an industrial heat transfer problem: the forced convective cooling of a LED-based spotlight. The design specification calls for eighteen diodes arranged on a circular copper plate of 35 mm diameter. Every diode dissipates 3 W and the maximum allowedtemperature of the plate is 80 °C. The cooling relies on the forced convection driven by a jet of air impinging on the plate. An initial complex geometry of plate fins is presented and analyzed with a commercial CFD code that computes the entropy generation rate. A pseudo-optimization process is carried out via a successive series of design modifications based on a careful analysis of the entropy generation maps. One of the advantages of the EGM method is that the rationale behind each step of the design process can be justified on a physical basis. It is found that the best performance is attained when the fins are periodically spaced in the radial direction.

Entropy, Vol. 13, Pages 1200-1211: Effective Complexity of Stationary Process Realizations

Nihat Ay — Wed, 22 Jun 2011 00:00:00 CEST

The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, which is the probability distributions on finite binary strings. In our previous paper [1] we propose a definition of effective complexity in precise terms of algorithmic information theory. Here we investigate the effective complexity of binary strings generated by stationary, in general not computable, processes. We show that under not too strong conditions long typical process realizations are effectively simple. Our results become most transparent in the context of coarse effective complexity which is a modification of the original notion of effective complexity that needs less parameters in its definition. A similar modification of the related concept of sophistication has been suggested by Antunes and Fortnow.

Entropy, Vol. 13, Pages 1186-1199: On the Thermodynamics of Classical Micro-Canonical Systems

Maarten Baeten — Tue, 21 Jun 2011 00:00:00 CEST

We give two arguments why the thermodynamic entropy of non-extensive systems involves R´enyi’s entropy function rather than that of Tsallis. The first argument is that the temperature of the configurational subsystem of a mono-atomic gas is equal to that of the kinetic subsystem. The second argument is that the instability of the pendulum, which occurs for energies close to the rotation threshold, is correctly reproduced.

Entropy, Vol. 13, Pages 1170-1185: Geometry of q-Exponential Family of Probability Distributions

Shun-ichi Amari — Tue, 14 Jun 2011 00:00:00 CEST

The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. We treat the q-Gibbs distribution or the q-exponential family by generalizing the exponential function to the q-family of power functions, which is useful for studying various complex or non-standard physical phenomena. We give a new mathematical structure to the q-exponential family different from those previously given. It has a dually flat geometrical structure derived from the Legendre transformation and the conformal geometry is useful for understanding it. The q-version of the maximum entropy theorem is naturally induced from the q-Pythagorean theorem. We also show that the maximizer of the q-escort distribution is a Bayesian MAP (Maximum A posteriori Probability) estimator.

Entropy, Vol. 13, Pages 1152-1169: EA/G-GA for Single Machine Scheduling Problems with Earliness/Tardiness Costs

Shih-Hsin Chen — Tue, 14 Jun 2011 00:00:00 CEST

An Estimation of Distribution Algorithm (EDA), which depends on explicitly sampling mechanisms based on probabilistic models with information extracted from the parental solutions to generate new solutions, has constituted one of the major research areas in the field of evolutionary computation. The fact that no genetic operators are used in EDAs is a major characteristic differentiating EDAs from other genetic algorithms (GAs). This advantage, however, could lead to premature convergence of EDAs as the probabilistic models are no longer generating diversified solutions. In our previous research [1], we have presented the evidences that EDAs suffer from the drawback of premature convergency, thus several important guidelines are provided for the design of effective EDAs. In this paper, we validated one guideline for incorporating other meta-heuristics into the EDAs. An algorithm named “EA/G-GA” is proposed by selecting a well-known EDA, EA/G, to work with GAs. The proposed algorithm was tested on the NP-Hard single machine scheduling problems with the total weighted earliness/tardiness cost in a just-in-time environment. The experimental results indicated that the EA/G-GA outperforms the compared algorithms statistically significantly across different stopping criteria and demonstrated the robustness of the proposed algorithm. Consequently, this paper is of interest and importance in the field of EDAs.

Entropy, Vol. 13, Pages 1137-1151: Maximum Profit Configurations of Commercial Engines

Yiran Chen — Tue, 07 Jun 2011 00:00:00 CEST

An investigation of commercial engines with finite capacity low- and high-price economic subsystems and a generalized commodity transfer law [n ∝ Δ (P m)] in commodity flow processes, in which effects of the price elasticities of supply and demand are introduced, is presented in this paper. Optimal cycle configurations of commercial engines for maximum profit are obtained by applying optimal control theory. In some special cases, the eventual state—market equilibrium—is solely determined by the initial conditions and the inherent characteristics of two subsystems; while the different ways of transfer affect the model in respects of the specific forms of the paths of prices and the instantaneous commodity flow, i.e., the optimal configuration.

Entropy, Vol. 13, Pages 1076-1136: A Philosophical Treatise of Universal Induction

Samuel Rathmanner — Fri, 03 Jun 2011 00:00:00 CEST

Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.

Entropy, Vol. 13, Pages 1055-1075: Distances in Probability Space and the Statistical Complexity Setup

Andres M. Kowalski — Fri, 03 Jun 2011 00:00:00 CEST

Statistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.

Entropy, Vol. 13, Pages 1034-1054: Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity

Mounir Bouabid — Mon, 23 May 2011 00:00:00 CEST

Thermosolutal convection in a square cavity filled with air and submitted to an inclined magnetic field is investigated numerically. The cavity is heated and cooled along the active walls with a mass gradient whereas the two other walls of the cavity are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Finite—Element Method. The structure of the studied flows depends on four dimensionless parameters which are the Grashof number, the buoyancy ratio, the Hartman number and the inclination angle. The results show that the magnetic field parameter has a retarding effect on the flow in the cavity and this lead to a decrease of entropy generation, Temperature and concentration decrease with increasing value of the magnetic field parameter.

Entropy, Vol. 13, Pages 1020-1033: Entropy Generation at Natural Convection in an Inclined Rectangular Cavity

Mounir Bouabid — Mon, 23 May 2011 00:00:00 CEST

Natural convection in an inclined rectangular cavity filled with air is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls of the cavity are adiabatic. Entropy generation due to heat transfer and fluid friction has been determined in transient state for laminar natural convection by solving numerically: the continuity, momentum and energy equations, using a Control Volume Finite Element Method. The structure of the studied flows depends on four dimensionless parameters which are: the thermal Grashof number, the inclination angle, the irreversibility distribution ratio and the aspect ratio of the cavity. The obtained results show that entropy generation tends towards asymptotic values for lower thermal Grashof number values, whereas it takes an oscillative behavior for higher values of thermal Grashof number. Transient entropy generation increases towards a maximum value, then decreases asymptotically to a constant value that depends on aspect ratio of the enclosure. Entropy generation increases with the increase of thermal Grashof number, irreversibility distribution ratio and aspect ratio of the cavity. Bejan number is used to measure the predominance of either thermal or viscous irreversibility. At local level, irreversibility charts show that entropy generation is mainly localized on bottom corner of the left heated wall and upper corner of the right cooled wall.

Entropy, Vol. 13, Pages 966-1019: The Michaelis-Menten-Stueckelberg Theorem

Alexander N. Gorban — Fri, 20 May 2011 00:00:00 CEST

We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

Entropy, Vol. 13, Pages 949-965: The Decoherence of the Electron Spin and Meta-Stability of 13C Nuclear Spins in Diamond

Peter Crompton — Thu, 05 May 2011 00:00:00 CEST

Following the recent successful experimental manipulation of entangled 13C atoms on the surface of Diamond, we calculate the decoherence of the electron spin in Nitrogen Vacancy NV centers of Diamond via a nonperturbative treatment of the time-dependent Greens function of a Central-Spin model in order to identify the Replica Symmetry Breaking mechanism associated with intersystem mixing between the ms = 0 sublevel of the 3A2 and 1A1 states of the NV− centers, which we identify as mediated via the meta-stability of 13C nuclei bath processes in our calculations. Rather than the standard exciton-based calculation scheme used for quantum dots, we argue that a new scheme is needed to formally treat the Replica Symmetry Breaking of the 3A2 → 3E excitations of the NV− centers, which we define by extending the existing Generalized Master Equation formalism via the use of fractional time derivatives. Our calculations allow us to accurately quantify the dangerously irrelevant scaling associated with the Replica Symmetry Breaking and provide an explanation for the experimentally observed room temperature stability of Diamond for Quantum Computing applications.

Entropy, Vol. 13, Pages 936-948: Is Gravity an Entropic Force?

Shan Gao — Thu, 28 Apr 2011 00:00:00 CEST

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This may provide a further support for the conclusion that gravity is not an entropic force.

Entropy, Vol. 13, Pages 924-935: Holographic Dark Information Energy

Michael Paul Gough — Thu, 21 Apr 2011 00:00:00 CEST

Landauer’s principle and the Holographic principle are used to derive the holographic information energy contribution to the Universe. Information energy density has increased with star formation until sufficient to start accelerating the expansion of the universe. The resulting reduction in the rate of star formation due to the accelerated expansion may provide a feedback that limits the information energy density to a constant level. The characteristics of the universe’s holographic information energy then closely match those required to explain dark energy and also answer the cosmic coincidence problem. Furthermore the era of acceleration will be clearly limited in time.

Entropy, Vol. 13, Pages 915-923: A Comment on Nadytko et al., “Amines in the Earth’s Atmosphere: A Density Functional Theory Study of the Thermochemistry of Pre-Nucleation Clusters”. Entropy 2011, 13, 554–569

Theo Kurtén — Tue, 19 Apr 2011 00:00:00 CEST

Nadykto, Yu, Jakovleva, Herb and Xu have recently reported a DFT study on the structure and formation thermodynamics of sulfuric acid-base-water clusters, with ammonia and a handful of amines as bases [1]. This study partially overlaps with our previous work [2], and a significant part of the discussion in their manuscript concerns differences between their results and ours. This comment is intended to address some issues related to that discussion. Specifically, it is shown that the errors related to basis-set effects in our calculations are very likely much smaller than claimed by Nadykto et al. [1]. Composite calculations including e.g., higher-level electron correlation also agree better with our results.

Entropy, Vol. 13, Pages 902-914: Algorithmic Relative Complexity

Daniele Cerra — Tue, 19 Apr 2011 00:00:00 CEST

Information content and compression are tightly related concepts that can be addressed through both classical and algorithmic information theories, on the basis of Shannon entropy and Kolmogorov complexity, respectively. The definition of several entities in Kolmogorov’s framework relies upon ideas from classical information theory, and these two approaches share many common traits. In this work, we expand the relations between these two frameworks by introducing algorithmic cross-complexity and relative complexity, counterparts of the cross-entropy and relative entropy (or Kullback-Leibler divergence) found in Shannon’s framework. We define the cross-complexity of an object x with respect to another object y as the amount of computational resources needed to specify x in terms of y, and the complexity of x related to y as the compression power which is lost when adopting such a description for x, compared to the shortest representation of x. Properties of analogous quantities in classical information theory hold for these new concepts. As these notions are incomputable, a suitable approximation based upon data compression is derived to enable the application to real data, yielding a divergence measure applicable to any pair of strings. Example applications are outlined, involving authorship attribution and satellite image classification, as well as a comparison to similar established techniques.

Entropy, Vol. 13, Pages 860-901: A Feature Subset Selection Method Based On High-Dimensional Mutual Information

Yun Zheng — Tue, 19 Apr 2011 00:00:00 CEST

Feature selection is an important step in building accurate classifiers and provides better understanding of the data sets. In this paper, we propose a feature subset selection method based on high-dimensional mutual information. We also propose to use the entropy of the class attribute as a criterion to determine the appropriate subset of features when building classifiers. We prove that if the mutual information between a feature set X and the class attribute Y equals to the entropy of Y , then X is a Markov Blanket of Y . We show that in some cases, it is infeasible to approximate the high-dimensional mutual information with algebraic combinations of pairwise mutual information in any forms. In addition, the exhaustive searches of all combinations of features are prerequisite for finding the optimal feature subsets for classifying these kinds of data sets. We show that our approach outperforms existing filter feature subset selection methods for most of the 24 selected benchmark data sets.

Entropy, Vol. 13, Pages 841-859: Optimal Multi-Level Thresholding Based on Maximum Tsallis Entropy via an Artificial Bee Colony Approach

Yudong Zhang — Wed, 13 Apr 2011 00:00:00 CEST

This paper proposes a global multi-level thresholding method for image segmentation. As a criterion for this, the traditional method uses the Shannon entropy, originated from information theory, considering the gray level image histogram as a probability distribution, while we applied the Tsallis entropy as a general information theory entropy formalism. For the algorithm, we used the artificial bee colony approach since execution of an exhaustive algorithm would be too time-consuming. The experiments demonstrate that: 1) the Tsallis entropy is superior to traditional maximum entropy thresholding, maximum between class variance thresholding, and minimum cross entropy thresholding; 2) the artificial bee colony is more rapid than either genetic algorithm or particle swarm optimization. Therefore, our approach is effective and rapid.

Entropy, Vol. 13, Pages 820-840: Some Convex Functions Based Measures of Independence and Their Application to Strange Attractor Reconstruction

Yang Chen — Fri, 08 Apr 2011 00:00:00 CEST

The classical information-theoretic measures such as the entropy and the mutual information (MI) are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO) and the quasientropy (QE) as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI). A quality factor (QF) is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.

Entropy, Vol. 13, Pages 805-819: Large-Sample Asymptotic Approximations for the Sampling and Posterior Distributions of Differential Entropy for Multivariate Normal Distributions

Guillaume Marrelec — Wed, 06 Apr 2011 00:00:00 CEST

In the present paper, we propose a large sample asymptotic approximation for the sampling and posterior distributions of differential entropy when the sample is composed of independent and identically distributed realization of a multivariate normal distribution.

Entropy, Vol. 13, Pages 790-804: Entropic Regularization to Assist a Geologist in Producing a Geologic Map

Valeria C.F. Barbosa — Wed, 06 Apr 2011 00:00:00 CEST

The gravity and magnetic data measured on the Earth’s surface or above it (collected from an aircraft flying at low altitude) can be used to assist in geologic mapping by estimating the spatial density and magnetization distributions, respectively, presumably confined to the interior of a horizontal slab with known depths to the top and bottom. To estimate density or magnetization distributions we assume a piecewise constant function defined on a user-specified grid of cells and invert the gravity or magnetic data by using the entropic regularization as a stabilizing function that allows estimating abrupt changes in the physical-property distribution. The entropic regularization combines the minimization of the first-order entropy measure with the maximization of the zeroth-order entropy measure of the solution vector. The aim of this approach is to detect sharp-bounded geologic units through the discontinuities in the estimated density or magnetization distributions. Tests conducted with synthetic data show that the entropic regularization can delineate discontinuous geologic units, allowing a better mapping of sharp-bounded (but buried) geologic bodies. We demonstrate the potential of the entropic regularization to assist a geologist in obtaining a geologic map by analyzing the estimated magnetization distributions from field magnetic data over a magnetic skarn in Butte Valley, Nevada, U.S.A. We show that it is an exoskarn where the ion exchange between the intrusive and the host rock occurs along a limited portion of the southern intrusive border.

Entropy, Vol. 13, Pages 778-789: Quantum Kolmogorov Complexity and Information-Disturbance Theorem

Takayuki Miyadera — Tue, 29 Mar 2011 00:00:00 CEST

In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vit´anyi has been examined. In the quantum information theory, the information-disturbance relationship, which treats the trade-off relationship between information gain and its caused disturbance, is a fundamental result that is related to Heisenberg’s uncertainty principle. The problem was formulated in a cryptographic setting and the quantitative relationships between complexities have been derived.

Entropy, Vol. 13, Pages 744-777: Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy

Alejandro Perez — Fri, 25 Mar 2011 00:00:00 CET

We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area aH of the horizon is fixed macroscopically—states with fluctuations away from spherical symmetry are allowed—we show that it is possible to obtain agreement with the Hawkings area law (S = aH /(4l 2p)) without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.

Entropy, Vol. 13, Pages 720-743: Analysis of Resource and Emission Impacts: An Emergy-Based Multiple Spatial Scale Framework for Urban Ecological and Economic Evaluation

Gengyuan Liu — Wed, 23 Mar 2011 00:00:00 CET

The development of the complex and multi-dimensional urban socio-economic system creates impacts on natural capital and human capital, which range from a local to a global scale. An emergy-based multiple spatial scale analysis framework and a rigorous accounting method that can quantify the values of human-made and natural capital losses were proposed in this study. With the intent of comparing the trajectory of Beijing over time, the characteristics of the interface between different scales are considered to explain the resource trade and the impacts of emissions. In addition, our improved determination of emergy analysis and acceptable management options that are in agreement with Beijing’s overall sustainability strategy were examined. The results showed that Beijing’s economy was closely correlated with the consumption of nonrenewable resources and exerted rising pressure on the environment. Of the total emergy use by the economic system, the imported nonrenewable resources from other provinces contribute the most, and the multi‑scale environmental impacts of waterborne and airborne pollution continued to increase from 1999 to 2006. Given the inputs structure, Beijing was chiefly making greater profits by shifting resources from other provinces in China and transferring the emissions outside. The results of our study should enable urban policy planners to better understand the multi-scale policy planning and development design of an urban ecological economic system.

Entropy, Vol. 13, Pages 709-719: Mode Switching and Collective Behavior in Chemical Oil Droplets

Naoto Horibe — Fri, 18 Mar 2011 00:00:00 CET

We have characterized several dynamic aspects of a simple chemical system capable of self-movement: An oil droplet in water system. We focused on spontaneous mode switching and collective behavior of droplets as emergent properties of the system. Droplets demonstrated spontaneous mode switching by changing speed, direction and acceleration over time, and collective behaviors of droplets resulted from such autonomous characteristics. In this paper, we quantitatively measured those characteristics to show that droplets did not act completely independently in the same system, but tend to be attracted to one another and interact with each other by adjusting their motion.

Entropy, Vol. 13, Pages 683-708: On a Connection between Information and Group Lattices

Hua Li — Fri, 18 Mar 2011 00:00:00 CET

In this paper we review a particular connection between information theory and group theory. We formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we expose a comprehensive parallelism between information lattices and subgroup lattices. Qualitatively, isomorphisms between information lattices and subgroup lattices are demonstrated. Quantitatively, a decisive approximation relation between the entropy structures of information lattices and the log-index structures of the corresponding subgroup lattices, first discovered by Chan and Yeung, is highlighted. This approximation, addressing both joint and common entropies, extends the work of Chan and Yeung on joint entropy. A consequence of this approximation result is that any continuous law holds in general for the entropies of information elements if and only if the same law holds in general for the log-indices of subgroups. As an application, by constructing subgroup counterexamples, we find surprisingly that common information, unlike joint information, obeys neither the submodularity nor the supermodularity law. We emphasize that the notion of information elements is conceptually significant—formalizing it helps to reveal the deep connection between information theory and group theory. The parallelism established in this paper admits an appealing group-action explanation and provides useful insights into the intrinsic structure among information elements from a group-theoretic perspective.

Entropy, Vol. 13, Pages 668-682: Did the Federal Agriculture Improvement and Reform Act of 1996 Affect Farmland Values?

Ashok K. Mishra — Thu, 17 Mar 2011 00:00:00 CET

Farmland values are affected by numerous factors, including farm policy, shifts in demand for agricultural output both foreign and domestic, monetary policy and urban pressure. In this study we use an information measure to examine whether the shift toward a more market-oriented policy in 1996 changed the relationship between farmland values and government payments. The results indicated that the shift in agricultural policy resulted in significant shift in this relationship.

Entropy, Vol. 13, Pages 650-667: k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions

Shengqiao Li — Tue, 08 Mar 2011 00:00:00 CET

A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable.

Entropy, Vol. 13, Pages 612-649: Information Theory and Dynamical System Predictability

Richard Kleeman — Mon, 07 Mar 2011 00:00:00 CET

Predicting the future state of a turbulent dynamical system such as the atmosphere has been recognized for several decades to be an essentially statistical undertaking. Uncertainties from a variety of sources are magnified by dynamical mechanisms and given sufficient time, compromise any prediction. In the last decade or so this process of uncertainty evolution has been studied using a variety of tools from information theory. These provide both a conceptually general view of the problem as well as a way of probing its non-linearity. Here we review these advances from both a theoretical and practical perspective. Connections with other theoretical areas such as statistical mechanics are emphasized. The importance of obtaining practical results for prediction also guides the development presented.

Entropy, Vol. 13, Pages 595-611: Entropy Measures vs. Kolmogorov Complexity

Andreia Teixeira — Thu, 03 Mar 2011 00:00:00 CET

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we show that, for some distributions we have a similar result. We prove that, for universal time-bounded distribution mt(x), Tsallis and Rényi entropies converge if and only if α is greater than 1. We also establish the uniform continuity of these entropies.

Entropy, Vol. 13, Pages 570-594: Towards an Evolutionary Model of Animal-Associated Microbiomes

Carl J. Yeoman — Fri, 25 Feb 2011 00:00:00 CET

Second-generation sequencing technologies have granted us greater access to the diversity and genetics of microbial communities that naturally reside endo- and ecto-symbiotically with animal hosts. Substantial research has emerged describing the diversity and broader trends that exist within and between host species and their associated microbial ecosystems, yet the application of these data to our evolutionary understanding of microbiomes appears fragmented. For the most part biological perspectives are based on limited observations of oversimplified communities, while mathematical and/or computational modeling of these concepts often lack biological precedence. In recognition of this disconnect, both fields have attempted to incorporate ecological theories, although their applicability is currently a subject of debate because most ecological theories were developed based on observations of macro-organisms and their ecosystems. For the purposes of this review, we attempt to transcend the biological, ecological and computational realms, drawing on extensive literature, to forge a useful framework that can, at a minimum be built upon, but ideally will shape the hypotheses of each field as they move forward. In evaluating the top-down selection pressures that are exerted on a microbiome we find cause to warrant reconsideration of the much-maligned theory of multi-level selection and reason that complexity must be underscored by modularity.

Entropy, Vol. 13, Pages 554-569: Amines in the Earth’s Atmosphere: A Density Functional Theory Study of the Thermochemistry of Pre-Nucleation Clusters

Alexey B. Nadykto — Mon, 21 Feb 2011 00:00:00 CET

The impact of organic species which are present in the Earth’s atmosphere on the burst of new particles is critically important for the understanding of the molecular nature of atmospheric nucleation phenomena. Amines have recently been proposed as possible stabilizers of binary pre-nucleation clusters. In order to advance the understanding of atmospheric nucleation phenomena, a quantum-chemical study of hydrogen-bonded complexes of binary sulfuric acid-water clusters with methyl-, dimethyl- and trimethylamines representing common atmospheric organic species, vegetation products and laboratory impurities has been carried out. The thermochemical stability of the sulfuric acid-amines-water complexes was found to be higher than that of the sulfuric acid-ammonia-water complexes, in qualitative agreement with the previous studies. However, the enhancement in stability due to amines appears to not be large enough to overcome the difference in typical atmospheric concentrations of ammonia and amines. Further research is needed in order to address the existing uncertainties and to reach a final conclusion about the importance of amines for the atmospheric nucleation.

Entropy, Vol. 13, Pages 542-553: Size Effects on the Entropy Production in Oscillatory Flow between Parallel Plates

Federico Vazquez — Fri, 18 Feb 2011 00:00:00 CET

The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the plates are also assessed. It is found that the global entropy production is a minimum for certain suitable combination of the physical parameters and a discrete set of values of the separation between the parallel plates. The transferred heat at the plates also shows minima in the same discrete set of values of the plates separation.

Entropy, Vol. 13, Pages 528-541: Entangled States in Quantum Cosmology and the Interpretation of Λ

Salvatore Capozziello — Thu, 17 Feb 2011 00:00:00 CET

The cosmological constant Λ can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., Ωm and Ωk, which assign the cosmic dynamics. In particular, we consider a cosmological model where two regions, corresponding to two correlated eras, are involved; the present universe description would be, in this way, given by a density matrix ˆρ, corresponding to an entangled final state. Starting from this assumption, it is possible to infer some considerations on the cosmic thermodynamics by evaluating the Von Neumann entropy. The correlation between different regions by the entanglement phenomenon results in the existence of Λ (in particular ΩΛ) which could be interpreted in the framework of the recent astrophysical observations. As a byproduct, this approach could provide a natural way to solve the so called coincidence problem.

Entropy, Vol. 13, Pages 518-527: The Nature of Stability in Replicating Systems

Nathaniel Wagner — Tue, 15 Feb 2011 00:00:00 CET

We review the concept of dynamic kinetic stability, a type of stability associated specifically with replicating entities, and show how it differs from the well-known and established (static) kinetic and thermodynamic stabilities associated with regular chemical systems. In the process we demonstrate how the concept can help bridge the conceptual chasm that continues to separate the physical and biological sciences by relating the nature of stability in the animate and inanimate worlds, and by providing additional insights into the physicochemical nature of abiogenesis.

Entropy, Vol. 13, Pages 502-517: Microcanonical Description of (Micro) Black Holes

Roberto Casadio — Mon, 14 Feb 2011 00:00:00 CET

The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g., negative specific heat (not allowed in the canonical ensemble) and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existenceis predicted in models with extra-spatial dimensions.

Entropy, Vol. 13, Pages 485-501: Estimating Neuronal Information: Logarithmic Binning of Neuronal Inter-Spike Intervals

Alan D. Dorval — Thu, 10 Feb 2011 00:00:00 CET

Neurons communicate via the relative timing of all-or-none biophysical signals called spikes. For statistical analysis, the time between spikes can be accumulated into inter-spike interval histograms. Information theoretic measures have been estimated from these histograms to assess how information varies across organisms, neural systems, and disease conditions. Because neurons are computational units that, to the extent they process time, work not by discrete clock ticks but by the exponential decays of numerous intrinsic variables, we propose that neuronal information measures scale more naturally with the logarithm of time. For the types of inter-spike interval distributions that best describe neuronal activity, the logarithm of time enables fewer bins to capture the salient features of the distributions. Thus, discretizing the logarithm of inter-spike intervals, as compared to the inter-spike intervals themselves, yields histograms that enable more accurate entropy and information estimates for fewer bins and less data. Additionally, as distribution parameters vary, the entropy and information calculated from the logarithm of the inter-spike intervals are substantially better behaved, e.g., entropy is independent of mean rate, and information is equally affected by rate gains and divisions. Thus, when compiling neuronal data for subsequent information analysis, the logarithm of the inter-spike intervals is preferred, over the untransformed inter-spike intervals, because it yields better information estimates and is likely more similar to the construction used by nature herself.

Entropy, Vol. 13, Pages 466-484: Primitive Membrane Formation, Characteristics and Roles in the Emergent Properties of a Protocell

Sarah Elizabeth Maurer — Thu, 10 Feb 2011 00:00:00 CET

All contemporary living cells are composed of a collection of self-assembled molecular elements that by themselves are non-living but through the creation of a network exhibit the emergent properties of self-maintenance, self-reproduction, and evolution. This short review deals with the on-going research that aims at either understanding how life emerged on the early Earth or creating artificial cells assembled from a collection of small chemicals. In particular, this article focuses on the work carried out to investigate how self-assembled compartments, such as amphiphile and lipid vesicles, contribute to the emergent properties as part of a greater system.

Entropy, Vol. 13, Pages 450-465: Information Theoretic Hierarchical Clustering

Mehdi Aghagolzadeh — Thu, 10 Feb 2011 00:00:00 CET

Hierarchical clustering has been extensively used in practice, where clusters can be assigned and analyzed simultaneously, especially when estimating the number of clusters is challenging. However, due to the conventional proximity measures recruited in these algorithms, they are only capable of detecting mass-shape clusters and encounter problems in identifying complex data structures. Here, we introduce two bottom-up hierarchical approaches that exploit an information theoretic proximity measure to explore the nonlinear boundaries between clusters and extract data structures further than the second order statistics. Experimental results on both artificial and real datasets demonstrate the superiority of the proposed algorithm compared to conventional and information theoretic clustering algorithms reported in the literature, especially in detecting the true number of clusters.

Entropy, Vol. 13, Pages 437-449: The Entropy of Progressively Censored Samples

Z. A. Abo-Eleneen — Wed, 09 Feb 2011 00:00:00 CET

In many life-testing and reliability studies, the experimenter might not always obtain complete information on failure times for all experimental units. Among the different censoring schemes, the progressive censoring scheme has received a considerable attention in the last few years. The aim of this paper is simplifying the entropy of progressively Type II censored samples. We propose an indirect approach using a decomposition of the entropy in progressively Type II censored samples to simplify the calculation. Some recurrence relations for the entropy in progressively Type II censored samples are derived to facilitate this calculation. An efficient computational method is derived that simplifies computation of the entropy in progressively Type II censored samples to a sum; entropy in collections order statistics. We compute the entropy in a collection of progressively Type II censored samples for some known distributions.

Entropy, Vol. 13, Pages 422-436: On the Dynamic Robustness of a Non-Endoreversible Engine Working in Different Operation Regimes

Norma Sanchez-Salas — Tue, 08 Feb 2011 00:00:00 CET

In this work, we focused mainly in the analysis of stability of a non-endoreversible Curzon-Ahlborn engine working in an ecological regime. For comparison purposes we also include the Maximum Efficient Power (MEP) regime taking into account the engine time delays. When the system’s dynamic stability is compared with its thermodynamics properties (efficiency and power output), we find that the temperature ratio τ = T1/T2 represents a trade-off between stability and energetic properties. When we take the non-endoreversible case, τ can increases to values greater than R (where R is the non-endoreversible parameter) but not greater than one. We reformulate an important difference between this case and the other two, Maximum Power (MP) and MEP regime, in which τ = R. Finally, we demonstrated that the total time delay does not destabilize the steady state of system. It does not seem to play a role in the dynamic thermodynamic property trade-off.

Entropy, Vol. 13, Pages 402-421: Deterministic Prediction of the Entropy Increase in a Sudden Expansion

LaVar King Isaacson — Mon, 31 Jan 2011 00:00:00 CET

This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in nature by invoking concepts from information theory to connect the deterministic prediction of the spectral entropy growth within the shear layer to the experimentally inferred increase in entropy across the flow region. The deterministic prediction of the spectral entropy increase along the shear layer is brought into agreement with the experimentally inferred increase in entropy through the ad hoc inclusion of the activation spectral entropy. The values for this activation spectral entropy are directly related to the area ratios across the expansion region and have a specific numerical value for each area ratio.

Entropy, Vol. 13, Pages 379-401: Recent Progresses in Characterising Information Inequalities

Terence Chan — Mon, 31 Jan 2011 00:00:00 CET

In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery of this non-Shannon inequality is a breakthrough in the area and has led to the subsequent discovery of many more non-Shannon inequalities. We will also review the close relations between information inequalities and other research areas such as Kolmogorov complexity, determinantal inequalities, and group-theoretic inequalities. These relations have led to non-traditional techniques in proving information inequalities and at the same time made impacts back onthose related areas by the introduction of information-theoretic tools.

Entropy, Vol. 13, Pages 367-378: Lagrange Equations Coupled to a Thermal Equation: Mechanics as Consequence of Thermodynamics

Christian Gruber — Mon, 31 Jan 2011 00:00:00 CET

Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential.

Entropy, Vol. 13, Pages 332-366: Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation

Claude Stolz — Mon, 31 Jan 2011 00:00:00 CET

The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.

Entropy, Vol. 13, Pages 316-331: Spin-Currents and Spin-Pumping Forces for Spintronics

Jean-Eric Wegrowe — Fri, 28 Jan 2011 00:00:00 CET

A general definition of the Spintronics concept of spin-pumping is proposed as generalized forces conjugated to the spin degrees of freedom in the framework of the theory of mesoscopic non-equilibrium thermodynamics. It is shown that at least three different kinds of spin-pumping forces and associated spin-currents can be defined in the most simple spintronics system: the Ferromagnetic/Non-Ferromagnetic metal interface. Furthermore, the generalized force associated with the ferromagnetic collective variable is also introduced on an equal footing to describe the coexistence of the spin of the conduction electrons (paramagnetic spins attached to s-band electrons) and the ferromagnetic-order parameter. The dynamical coupling between these two kinds of magnetic degrees of freedom is presented and interpreted in terms of spin-transfer effects.

Entropy, Vol. 13, Pages 293-315: A Maximum Entropy Modelling of the Rain Drop Size Distribution

Ramiro Checa — Wed, 26 Jan 2011 00:00:00 CET

This paper presents a maximum entropy approach to Rain Drop Size Distribution (RDSD) modelling. It is shown that this approach allows (1) to use a physically consistent rationale to select a particular probability density function (pdf) (2) to provide an alternative method for parameter estimation based on expectations of the population instead of sample moments and (3) to develop a progressive method of modelling by updating the pdf as new empirical information becomes available. The method is illustrated with both synthetic and real RDSD data, the latest coming from a laser disdrometer network specifically designed to measure the spatial variability of the RDSD.