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Open AccessEditorial

Foreword: Proceedings of the 4th International Electronic Conference on Entropy and Its Applications

by Philip Broadbridge

Proceedings 2018, 2(4), 196; https://doi.org/10.3390/proceedings2040196 - 24 Jan 2018

Viewed by 1503

Abstract

This volume presents papers contributed to the 4th E-Conference on Entropy (ECEA-4), of November 2017. [...] Full article

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8 pages, 518 KiB

Open AccessProceeding Paper

An Evaluation of Heat Transfer Enhancement Technique in Flow Boiling Conditions Based on Entropy Generation Analysis: Micro-Fin Tube

by Mohammad Ali Abdous

Proceedings 2018, 2(4), 149; https://doi.org/10.3390/ecea-4-05002 - 20 Nov 2017

Cited by 3 | Viewed by 1755

Abstract

The flow boiling heat transfer is one of the common phenomenon happening in the industries. The micro-fin tubes are one of the geometries widely used to enhance heat transfer rate in boiling condition. The entropy generation analysis is presented with its formulation to [...] Read more.

The flow boiling heat transfer is one of the common phenomenon happening in the industries. The micro-fin tubes are one of the geometries widely used to enhance heat transfer rate in boiling condition. The entropy generation analysis is presented with its formulation to find precisely the best operating conditions in micro-fin tubes in terms of geometrical parameters and flow conditions. This analysis shows important aspects of losses in fluid systems undergoing boiling. The losses include thermal loss related to the heat transfer and hydraulic one related to the pressure drop. The relevant terms are described for both of these losses. The optimum tube diameter under specified conditions is found. The effect of different flow conditions such as mass velocity, inlet vapor quality on contribution of pressure drop and heat transfer in entropy generation is discussed. It is discovered that there is a desirable set of conditions of fluid flow and micro-fin geometrical shape for which the minimum entropy generation is reached. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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11 pages, 4718 KiB

Open AccessProceeding Paper

Zeeman Effects on the Entanglement of Non-Equilibrium Finite-Spin Systems

by Koichi Nakagawa

Proceedings 2018, 2(4), 150; https://doi.org/10.3390/ecea-4-05003 - 20 Nov 2017

Viewed by 1456

Abstract

We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD). For this purpose, the extended density matrices and extended entanglement entropies of two systems with either non-competing or competing external fields [...] Read more.

We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD). For this purpose, the extended density matrices and extended entanglement entropies of two systems with either non-competing or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared. Consequently, through the “twin-peaks” oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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11 pages, 490 KiB

Open AccessProceeding Paper

Information Entropy of Molecular Tunneling

by Anatoly V. Stepanov and Maxim A. Stepanov

Proceedings 2018, 2(4), 151; https://doi.org/10.3390/ecea-4-05005 - 20 Nov 2017

Cited by 1 | Viewed by 1459

Abstract

Molecular tunneling process has been considered by means of radiation theory. The formula for information entropy calculation has been derived by means of interaction model of thermal equilibrium radiation with a molecule at low temperatures. The physical meaning of information entropy for low-temperature [...] Read more.

Molecular tunneling process has been considered by means of radiation theory. The formula for information entropy calculation has been derived by means of interaction model of thermal equilibrium radiation with a molecule at low temperatures. The physical meaning of information entropy for low-temperature plateau of unimolecular chemical reaction has been determined. It is a measure of conversion of thermal radiation energy to mechanical energy that moves atoms in a molecule during elementary activation act. It is also a measure of uncertainty of this energy conversion. The conversion takes place at a temperature when the average energy of the elementary activation act is equal to a part of zero energy of the transforming molecule. Two unimolecular reactions have been investigated. These are Fe-CO bond recombination in β-hemoglobin and double proton transfer in benzoic acid dimer for sequential deuteration of hydrogen bond and various hydrostatic pressures. Using the information entropy formula it is possible to calculate its value in energy units of measurements for low-temperature plateau. Probabilities of occurrence of the reactions under considerations, their efficiency and mean-square fluctuations of the distribution function parameters have also been determined. Full article

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16 pages, 622 KiB

Open AccessProceeding Paper

Interpolating Binary and Multivalued Logical Quantum Gates

by Zeno Toffano and François Dubois

Proceedings 2018, 2(4), 152; https://doi.org/10.3390/ecea-4-05006 - 20 Nov 2017

Cited by 2 | Viewed by 1855

Abstract

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding [...] Read more.

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding to all the one-argument logical connectives. Scaling-up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean functions is presented and a Reed-Muller decomposition for quantum logical gates is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate-T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders. Full article

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12 pages, 1920 KiB

Open AccessProceeding Paper

Entropy and Geometric Objects

by Georg J. Schmitz

Proceedings 2018, 2(4), 153; https://doi.org/10.3390/ecea-4-05007 - 20 Nov 2017

Viewed by 2568

Abstract

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense; (ii) the information sense; (iii) the statistical sense; (iv) the disorder sense; and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require [...] Read more.

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense; (ii) the information sense; (iii) the statistical sense; (iv) the disorder sense; and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass; a momentum; a temperature; a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast; the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length-and a factor 1/4. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function; with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local; statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations. Full article

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8 pages, 244 KiB

Open AccessProceeding Paper

Maxwell’s Demon and Comoving Observers in General Relativity: What Do They Have in Common?

by Luis Herrera

Proceedings 2018, 2(4), 154; https://doi.org/10.3390/ecea-4-05032 - 21 Nov 2017

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Abstract

We elaborate on the similarities between the explanation of the well known Maxwell’s demon paradox, based on the theory of information, and the rationale behind the fact that real dissipative (entropy producing) processes may be detected by non–comoving observers (tilted), in systems that [...] Read more.

We elaborate on the similarities between the explanation of the well known Maxwell’s demon paradox, based on the theory of information, and the rationale behind the fact that real dissipative (entropy producing) processes may be detected by non–comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

5 pages, 229 KiB

Open AccessProceeding Paper

Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology

by Pedro Fernández De Córdoba and Jose Maria Isidro San Juan

Proceedings 2018, 2(4), 155; https://doi.org/10.3390/ecea-4-05008 - 21 Nov 2017

Viewed by 1375

Abstract

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around

10^{123} k_{B}

(

k_{B}

being Boltzmann’s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum [...] Read more.

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around

10^{123} k_{B}

(

k_{B}

being Boltzmann’s constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation. One proves that the equations governing the cosmological fluid (the Euler equation and the continuity equation) become the very equations that govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy of a Newtonian Universe. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

16 pages, 357 KiB

Open AccessProceeding Paper

Exponential or Power Law? How to Select a Stable Distribution of Probability in a Physical System

by Andrea Di Vita

Proceedings 2018, 2(4), 156; https://doi.org/10.3390/ecea-4-05009 - 20 Nov 2017

Cited by 1 | Viewed by 1928

Abstract

A mapping of non-extensive statistical mechanics with non-additivity parameter

q \neq 1

into Gibbs’ statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to

q \neq 1

both of Einstein’s formula for fluctuations and of the ’general [...] Read more.

A mapping of non-extensive statistical mechanics with non-additivity parameter

q \neq 1

into Gibbs’ statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to

q \neq 1

both of Einstein’s formula for fluctuations and of the ’general evolution criterion’ (P. Glansdorff, I. Prigogine, Physica 30 351 (1964)), an inequality involving the time derivatives of thermodynamical quantities. Unified thermodynamic description of relaxation to stable states with either Boltzmann (

q = 1

) or power-law (

q \neq 1

) distribution of probabilities of microstates follows. If a 1D (possibly nonlinear) Fokker-Planck equation describes relaxation, then generalized Einstein’s formula predicts whether the relaxed state exhibits a Boltzmann or a power law distribution function. If this Fokker-Planck equation is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete, noise-affected map, then we may ascertain if a a relaxed state follows a power-law statistics—and with which exponent—by looking at both map dynamics and noise level, without assumptions concerning the (additive or multiplicative) nature of the noise and without numerical computation of the orbits. Results agree with the simulations (J. R. Sánchez, R. Lopez-Ruiz, EPJ 143.1 (2007): 241–243) of relaxation leading to a Pareto-like distribution function. Full article

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5 pages, 241 KiB

Open AccessProceeding Paper

Causal Classical Physics in Time Symmetric Quantum Mechanics

by Fritz W. Bopp

Proceedings 2018, 2(4), 157; https://doi.org/10.3390/ecea-4-05010 - 20 Nov 2017

Cited by 2 | Viewed by 1708

Abstract

The letter submitted is an executive summary of our previous paper. To solve the Einstein Podolsky Rosen “paradox” the two boundary quantum mechanics is taken as self consistent interpretation of quantum dynamics. The difficulty with this interpretation is to reconcile it with classical [...] Read more.

The letter submitted is an executive summary of our previous paper. To solve the Einstein Podolsky Rosen “paradox” the two boundary quantum mechanics is taken as self consistent interpretation of quantum dynamics. The difficulty with this interpretation is to reconcile it with classical physics. To avoid macroscopic backward causation two “corresponding transition rules” are formulated which specify needed properties of macroscopic observations and manipulations. The apparent classical causal decision tree requires to understand the classically unchosen options. They are taken to occur with an “incomplete knowledge” of the boundary states typically in macroscopic considerations. The precise boundary conditions with given phases then select the actual measured path and this selection is mistaken to happen at the time of measurement. The apparent time direction of the decision tree originates in an assumed relative proximity to the initial state. Only the far away final state allows for classically distinct options to be selected from. Cosmologically the picture could correspond to a big bang initial and a hugely extended final state scenario. It is speculated that it might also hold for a big bang/big crunch world. If this would be the case the Born probability postulate could find a natural explanation if we coexist in the expanding and the correlated CPT conjugate contracting world. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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5 pages, 359 KiB

Open AccessProceeding Paper

Maximum Entropy Production Principle and Morphological Selection in Hydrodynamic Systems

by Anna Birzina and Leonid Martyushev

Proceedings 2018, 2(4), 158; https://doi.org/10.3390/ecea-4-05011 - 20 Nov 2017

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Abstract

In recent decades an idea has emerged that the maximum entropy production principle can be used to select from the different regimes of development of nonequilibrium systems. According to this principle the process with maximum entropy production is most preferred among the possible [...] Read more.

In recent decades an idea has emerged that the maximum entropy production principle can be used to select from the different regimes of development of nonequilibrium systems. According to this principle the process with maximum entropy production is most preferred among the possible non-equilibrium processes. As a consequence, entropy production can be used to find an actually observed pattern formation among the hypothetical ones. A hypothesis is introduced that entropy production can be used to find a boundary (binodal) dividing the region of absolutely stable growth from the region of growth which is unstable (metastable) with regard to arbitrary amplitude distortions. This principle has been successfully applied to analyze the interfacial morphological stability during crystallization. The objective of this study is an application of described principle in two cases. The first problem is the stability analysis of the displacement front of two fluids in the radial Hele-Shaw cell. Together with linear stability analysis (which describes the stability to infinitesimal distortions, i.e., gives the spinodal) entropy production approach allows to determinate the region of different interface forms coexistence. These boundaries are analyzed depending on the cell size, the injected flow rate, and the ratio of the fluid viscosities. The second problem is the stability of a spherical surface of a vapor bubble growing under inertia control. In this case we obtain that the entropy production in the vicinity of the bubble’s distorted surface is always greater than that of the undistorted surface. Such a result indicates that the morphological phase with a distorted surface is more preferable and consequently should be observable in a real system where arbitrary perturbations occur. This allows explaining the experimentally observed roughness of the bubble surface during explosive vaporization. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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10 pages, 747 KiB

Open AccessProceeding Paper

Sustainability Enhancement of a Biomass Boiler through Exergy Analysis

by Marc Compton and Behnaz Rezaie

Proceedings 2018, 2(4), 159; https://doi.org/10.3390/ecea-4-05012 - 20 Nov 2017

Cited by 4 | Viewed by 2087

Abstract

Investigations on exergy resources are important from the point of energy sustainability. In the presented study, an energy and exergy analysis of the operating biomass and natural gas boilers at the University of Idaho (UI) district energy plant is conducted. Exergy flows through [...] Read more.

Investigations on exergy resources are important from the point of energy sustainability. In the presented study, an energy and exergy analysis of the operating biomass and natural gas boilers at the University of Idaho (UI) district energy plant is conducted. Exergy flows through the components of the steam cycle associated with the biomass boiler are quantified to identify major sources of exergy destruction in the district heating system. It is found that the biomass boiler has reduced energy and exergy efficiency compared to the natural gas boilers. Thermal efficiency varies from 76 to 85%, while exergy efficiency is significantly lower at 24 to 27% for all the boilers. Exergy accounting reveals that the biomass boiler and furnace account for the greatest exergy destruction, at approximately 68% of the exergy provided by the fuel. Steam use on campus represents about 6% of exergy losses while the pressure reducer is responsible for 4%. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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4 pages, 294 KiB

Open AccessProceeding Paper

The Relationship between the US Economy’s Information Processing and Absorption Ratio’s

by Edgar Parker

Proceedings 2018, 2(4), 160; https://doi.org/10.3390/ecea-4-05013 - 20 Nov 2017

Viewed by 1533

Abstract

After the 2008 financial collapse, Kritzman et al. 2010 introduced the now popular measure of implied systemic risk called the absorption ratio. This statistic is constructed from a fixed number of eigenvectors, and measures how closely the economy’s markets are coupled. The more [...] Read more.

After the 2008 financial collapse, Kritzman et al. 2010 introduced the now popular measure of implied systemic risk called the absorption ratio. This statistic is constructed from a fixed number of eigenvectors, and measures how closely the economy’s markets are coupled. The more closely financial markets are coupled the more susceptible they are to systemic collapse. Parker 2017 utilized information theory to develop the concept of entropic yield curve. From this equation, the implied information processing ratio or entropic efficiency of the economy can be derived. This entropic measure can also be useful in predicting economic downturns. In the current work, the relationship between these two ratios is explored. Full article

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18 pages, 3589 KiB

Open AccessProceeding Paper

Irreversibility of the Direct and Counter Impinging Liquid Jet onto Profiled Heated Cavity

by Fikret Alic

Proceedings 2018, 2(4), 161; https://doi.org/10.3390/ecea-4-05014 - 20 Nov 2017

Viewed by 1560

Abstract

Liquid impinging jet at the bottom of the annular cavity is a typical case in the process industry. The jet could have an impact at the bottom center or its peripheral section. The profiled annular cylindrical cavity with the installed electricity heater source [...] Read more.

Liquid impinging jet at the bottom of the annular cavity is a typical case in the process industry. The jet could have an impact at the bottom center or its peripheral section. The profiled annular cylindrical cavity with the installed electricity heater source is investigated in this paper. Thermal contact irreversibility and liquid drag irreversibility are generated within the profiled cavity. Through analytical modeling and experimental verification, a valid model of the entropy generation is established for both states. The results show that the total entropy between the liquid and the bottom is many times greater for the case of the central jet impingement. Within the annular vertical walls are the locations of the maximum or minimum of the entropy. The effectiveness of the liquid heating is greater in the peripheral impact of the liquid. The method and the results are the basis for optimizing the profiled cavity in various optimization geometry parameters. The optimal geometry of the annular cavity exists in such a way that the balance between thermal irreversibility and liquid drag irreversibility leads to the total minimum rate of the entropy generation for the annular cavity. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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7 pages, 336 KiB

Open AccessProceeding Paper

A Lower Bound on Work Extraction Probability Prescribed by Nonequilibrium Work Relation

by Takuya Yamano

Proceedings 2018, 2(4), 162; https://doi.org/10.3390/ecea-4-05015 - 20 Nov 2017

Cited by 2 | Viewed by 1500

Abstract

In nonequilibrium processes, work extraction from a system is subject to random fluctuations associated with the statistical distribution prescribed by its environment. The probability of extracting work above a given arbitrary threshold can be a measure of restriction imposed by experimental circumstances. We [...] Read more.

In nonequilibrium processes, work extraction from a system is subject to random fluctuations associated with the statistical distribution prescribed by its environment. The probability of extracting work above a given arbitrary threshold can be a measure of restriction imposed by experimental circumstances. We present a lower bound for the probability when the work value lies in a finite range. For the case of fixed maximum work, the lower bound gets larger as the free energy difference between initial and final states becomes larger. We point out also that an upper bound previously reported in the literature is a direct consequence of the well-known second mean value theorem for definite integrals. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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5 pages, 253 KiB

Open AccessProceeding Paper

A Comparison between Wasserstein Distance and a Distance Induced by Fisher-Rao Metric in Complex Shapes Clustering

by Angela De Sanctis and Stefano A. Gattone

Proceedings 2018, 2(4), 163; https://doi.org/10.3390/ecea-4-05016 - 20 Nov 2017

Cited by 1 | Viewed by 2125

Abstract

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a human head in the space. The applications range from structural biology, computer vision, medical imaging to archaeology. We focus on the selection of an appropriate measurement of [...] Read more.

Shape Analysis studies geometrical objects, as for example a flat fish in the plane or a human head in the space. The applications range from structural biology, computer vision, medical imaging to archaeology. We focus on the selection of an appropriate measurement of distance among observations with the aim of obtaining an unsupervised classification of shapes. Data from a shape are often realized as a set of representative points, called landmarks. For planar shapes, we assume that each landmark is modeled via a bivariate Gaussian, where the means capture uncertainties that arise in landmarks placement and the variances the natural variability across the population of shapes. At first we consider the Fisher-Rao metric as a Riemannian metric on the Statistical Manifold of the Gaussian distributions. The induced geodesic-distance is related with the minimization of information in the Fisher sense and we can use it to discriminate shapes. Another suitable distance is the Wasserstein distance, which is induced by a Riemannian metric and is related with the minimal transportation cost. In this work, a simulation study is conducted in order to make a comparison between Wasserstein and Fisher-Rao metrics when used in shapes clustering. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

10 pages, 308 KiB

Open AccessProceeding Paper

Characterization of Some Dynamic Network Models

by Pedro J. Zufiria and Iker Barriales-Valbuena

Proceedings 2018, 2(4), 164; https://doi.org/10.3390/ecea-4-05031 - 21 Nov 2017

Viewed by 1282

Abstract

Dynamic random network models are presented as a mathematical framework for modelling and analyzing the time evolution of complex networks. Such framework allows the time analysis of several network characterizing features such as link density, clustering coefficient, degree distribution, as well as entropy-based [...] Read more.

Dynamic random network models are presented as a mathematical framework for modelling and analyzing the time evolution of complex networks. Such framework allows the time analysis of several network characterizing features such as link density, clustering coefficient, degree distribution, as well as entropy-based complexity measures, providing new insight on the evolution of random networks. Some simple dynamic models are analyzed with the aim to provide several basic reference evolution behaviors. Simulation examples are discussed to illustrate the applicability of the proposed framework. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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10 pages, 381 KiB

Open AccessProceeding Paper

Information Theory for Equalizing the Residue-Wise Information Amounts of the Proteins and Protein-Coding DNA

by Yekbun Adiguzel

Proceedings 2018, 2(4), 165; https://doi.org/10.3390/ecea-4-05017 - 20 Nov 2017

Cited by 1 | Viewed by 1529

Abstract

Information content of a polymeric macromolecule can be calculated in bits, by multiplying the number of building blocks that encompasses the entire length of the macromolecule with the Shannon’s entropy of each building block, which could be determined through the degree of variation [...] Read more.

Information content of a polymeric macromolecule can be calculated in bits, by multiplying the number of building blocks that encompasses the entire length of the macromolecule with the Shannon’s entropy of each building block, which could be determined through the degree of variation (in the number) of those building blocks. DNA and the proteins that are encoded by genes, which are certain protein-coding regions of the DNA, are also polymeric macromolecules that are comprised of such building blocks, named residues. However, there is seemingly lower residue-based information amount in the protein if the mentioned approach is applied to a protein of specific size and the DNA that would be encoding the same length of a protein. Accordingly, this work initially presents the attempt to eliminate the decrease in the information amount of the protein by implementation of a new parameter in the calculation with the assumption that the information is not lost (or gained) during the protein translation process. An important additional biological significance of the work is revealed during latter calculations for the equalization of the information amounts in the protein and DNA molecules, which is the resolution of the problem of the presence of immense variation in the sizes of the proteins by accounting for the presence of introns in the eukaryotic genome. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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6 pages, 259 KiB

Open AccessProceeding Paper

On a General Definition of Conditional Rényi Entropies

by Velimir M. Ilić, Ivan B. Djordjević and Miomir Stanković

Proceedings 2018, 2(4), 166; https://doi.org/10.3390/ecea-4-05030 - 21 Nov 2017

Cited by 6 | Viewed by 1903

Abstract

In recent decades, different definitions of conditional Rényi entropy (CRE) have been introduced. Thus, Arimoto proposed a definition that found an application in information theory, Jizba and Arimitsu proposed a definition that found an application in time series analysis and Renner-Wolf, Hayashi and [...] Read more.

In recent decades, different definitions of conditional Rényi entropy (CRE) have been introduced. Thus, Arimoto proposed a definition that found an application in information theory, Jizba and Arimitsu proposed a definition that found an application in time series analysis and Renner-Wolf, Hayashi and Cachin proposed definitions that are suitable for cryptographic applications. However, there is still no a commonly accepted definition, nor a general treatment of the CRE-s, which can essentially and intuitively be represented as an average uncertainty about a random variable X if a random variable Y is given. In this paper we fill the gap and propose a three-parameter CRE, which contains all of the previous definitions as special cases that can be obtained by a proper choice of the parameters. Moreover, it satisfies all of the properties that are simultaneously satisfied by the previous definitions, so that it can successfully be used in aforementioned applications. Thus, we show that the proposed CRE is positive, continuous, symmetric, permutation invariant, equal to Rényi entropy for independent X and Y, equal to zero for

X = Y

and monotonic. In addition, as an example for the further usage, we discuss the properties of generalized mutual information, which is defined using proposed CRE. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

10 pages, 376 KiB

Open AccessProceeding Paper

Beyond the Arrow of Time: Can There Be a Relation between the Measurement of Entropy and Time?

by Ben Akih-Kumgeh

Proceedings 2018, 2(4), 167; https://doi.org/10.3390/ecea-4-05018 - 20 Nov 2017

Viewed by 1644

Abstract

The general tendency of the entropy of an isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be [...] Read more.

The general tendency of the entropy of an isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be measured by measuring entropy change and vice versa. The existence or absence of such a link also calls for further consideration of the nature of time. Prigogine argued that the true nature of time can only be discovered by investigating this phenomenon using scientific and philosophical methods. If this is true, then ongoing debates in the metaphysics of time and progress in the scientific study of entropy can be brought together to shed light on this fascinating but elusive concept. In this paper, starting from my recent modified definition of entropy change as a non-dimensional measure of energy change, a direct link between entropy and time duration is suggested. It draws from steady energy transfer processes such as heat transfer and shows that a measure of time can be found to be associated with a measure of entropy change. In the absence of other driving forces, the passage of time in an isolated system can therefore be tracked with a well calibrated entropy change meter. When other forces are allowed to interfere and there is no external point from which the system can be considered to be isolated, then the measure of time is non-monotonous since an isolated system can be restored to an earlier state of non-equilibrium. More philosophical questions about time can be reduced to questions about the operation of memory and consciousness, whereby psychological awareness of time is in essence a mental awareness of the way things are ordered by direct perception and memory of how they were ordered in the past, permitting a measure of the departure between things changing with greater or lesser intensity. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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9 pages, 699 KiB

Open AccessProceeding Paper

Entropy in Multiple Equilibria, Systems with Two Different Sites

by Gion Calzaferri

Proceedings 2018, 2(4), 168; https://doi.org/10.3390/ecea-4-05019 - 20 Nov 2017

Viewed by 1495

Abstract

The influence of entropy in multiple chemical equilibria is investigated for systems with two different types of sites for Langmuir’s condition, which means that the binding enthalpy of the species is the same for each type of sites and independent of those that [...] Read more.

The influence of entropy in multiple chemical equilibria is investigated for systems with two different types of sites for Langmuir’s condition, which means that the binding enthalpy of the species is the same for each type of sites and independent of those that are already bonded and that this holds for both types of sites independently. The analysis makes use of the particle distribution theory which holds for each type of sites separately. We provide physical insight by discussing an X_m{AB}X_n system with m = 0, 1, …, M and n = 0, 1, …, N in detail. The procedure and results are exemplified for an X_m{AB}X_n system with M = 3 and N = 2. A satisfactory consequence of the results is that the eleven equilibrium constants needed to describe such a system can be expressed as a function of two constants only. This is generally valid for any X_m{AB}X_n system where the [(M + 1)(N + 1) − 1] equilibrium constants can be expressed as a function of 2 constants only. This has also implication for quantum-theoretical studies in the sense that it is sufficient to model only two reactions instead of many in order to describe the system. We have observed that it is sufficient to have two different sites in a multiple equilibrium in order to observe a characteristic of isotherms that cannot be described by Langmuir’s equation. This is a result that may be useful for explaining experimental data which otherwise have not been explained satisfactory so far. Instead of inventing adsorption models it might often make sense of describing the system in terms of multiple equilibria. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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7 pages, 464 KiB

Open AccessProceeding Paper

Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

by Octavio Obregón and Marco Ortega-Cruz

Proceedings 2018, 2(4), 169; https://doi.org/10.3390/ecea-4-05020 - 20 Nov 2017

Cited by 2 | Viewed by 1461

Abstract

Modified entropies have been extensively considered by several authors in articles published almost anywhere. Among the most well known are the Rényi entropy and the Havdra-Charvtá and Tsallis entropy. All these depend on one or several parameters. By means of a modification to [...] Read more.

Modified entropies have been extensively considered by several authors in articles published almost anywhere. Among the most well known are the Rényi entropy and the Havdra-Charvtá and Tsallis entropy. All these depend on one or several parameters. By means of a modification to Superstatistics, one of the authors (Obregón) has proposed generalized entropies that depend only on the probability. There are three entropies:

S_{I} = k \sum_{l = 1}^{Ω} (1 - p_{l}^{p_{l}})

,

S_{I I} = k \sum_{l = 1}^{Ω} (p_{l}^{- p_{l}} - 1)

and their linear combination

S_{I I I} = k \sum_{l = 1}^{Ω} \frac{p_{l}^{- p_{l}} - p_{l}^{p_{l}}}{2}

. It is interesting to notice that the expansion in series of these entropies having as a first term

S = - k \sum_{l = 1}^{Ω} p_{l} ln p_{l}

in the parameter

x_{_{l}} \equiv p_{l} ln p_{l} \leq 1

cover, up to the first terms, any other expansion of any other possible function in

x_{_{l}}

, one would want to propose as another entropy. The three proposed entropies by Obregón are then the only possible generalizations of the Boltzmann-Gibbs (BG) or Shannon entropies that depend only of the probability. One obtains a superposition of two statistics (that of

β

and that of

p_{l}

), hence the name superstatistics. One may define an averaged Boltzmann factor as

B (E) = \int_{0}^{\infty} f (β) e^{β E} d β

where

f (β)

is the distribution of

β

. This work will deal with the analysis of the first two generalized entropies and will propose and deduce their associated quantum statistics; namely Bose-Einstein and Fermi-Dirac. The results will be compared with the standard ones and those due to the entropies by Tsallis. It will be seen in both cases that the BEO (the Bose-Einstein statistics corresponding to the entropies proposed by Obregón) statistic differs slightly from the usual BE statistic and in the same way for FDO the difference is small from the usual FD. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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12 pages, 763 KiB

Open AccessProceeding Paper

Entropy Production in the Expanding Universe

by Mehrnoosh Farahmand and Hosein Mohammadzadeh

Proceedings 2018, 2(4), 170; https://doi.org/10.3390/ecea-4-05037 - 23 Nov 2017

Viewed by 1636

Abstract

The spacetime is basically curved and dynamical. Thus our knowledge of universe must be extended to a dynamical curved spacetime to understand the nature of the universe. The field theory in the curved spacetime has shown that the evolution of spacetime involving the [...] Read more.

The spacetime is basically curved and dynamical. Thus our knowledge of universe must be extended to a dynamical curved spacetime to understand the nature of the universe. The field theory in the curved spacetime has shown that the evolution of spacetime involving the field in the curved spacetime leads to particle creation. From another perspective, by employing thermodynamics to cosmology, we can learn about the source of current entropy content associated with the universe. From the quantum thermodynamics, it is clear that the inner friction stemming from the quantum fluctuations of the field can produce the entropy. Using this approach, the particle creation due to the expansion of spacetime beginning from the vacuum is shown as an entropic increase. Considering an asymptotically flat Robertson-Walker spacetime, the particle creation entropy is evaluated. Each special scale factor can be used to characterize the cosmic parameters. Thus, the dependence of particle creation entropy on the field parameters and the cosmic parameters allows us to recover information from the underlying structure of the spacetime. Also, by adding an entropy production, indicating the mutual information between created particle and spacetime, to this particle creation entropy, the well-known entanglement measure can obtained to investigate the entanglement of created particles. In fact, the entanglement entropy, measuring the mixedness of the primary state, is affected from the creation and the correlation of the particle. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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14 pages, 400 KiB

Open AccessProceeding Paper

Performance Analysis of Single Glazed Solar PVT Air Collector in the Climatic Condition of NE India

by Biplab Das, Behnaz Rezaie, Prabhakar Jha and Rajat Gupta

Proceedings 2018, 2(4), 171; https://doi.org/10.3390/ecea-4-05021 - 20 Nov 2017

Cited by 7 | Viewed by 2005

Abstract

With the rapid depletion of fossils fuels, opportunities for renewable energy including solar energy are endless. The efficiency of photovoltaic cells to convert the solar energy into electricity drops with the rise in temperature due to increased resistance. Thus, improving the efficiency by [...] Read more.

With the rapid depletion of fossils fuels, opportunities for renewable energy including solar energy are endless. The efficiency of photovoltaic cells to convert the solar energy into electricity drops with the rise in temperature due to increased resistance. Thus, improving the efficiency by lowering the thermal resistance and allowing the cooling fluid (air/water) to flow through photovoltaic thermal (PVT) system is an attractive option. Climate condition based performance of any PVT system varies location wise, and cannot be generalized. Silchar is a city located in Himalayan region has tropical climatic conditions and most of its decentralized villages are out of grid connectivity. Unlike other metro cities of India, PVT will play a critical role for the development of theses villages. Keeping this in mind an attempt is made in the present study to perform an analysis of single glazed solar PVT air collector on the basis of energy and exergy for the climatic conditions of Silchar, India. An analytical model is developed to evaluate the hourly variation of PV cell temperature, cell efficiency, useful thermal heat gain, useful electrical heat gain, energy efficiency and exergy efficiency PVT system. Results depict that efficiency of PV cell decreases with the increase in temperature, and a maximum efficiency of 14.6% for the PV module is found. Out of total useful heat output, the thermal heat output contributes 60.7% while the rest is electrical heat output. Further, magnitude of the heat output is found to increase with the solar radiation and the maximum observed solar ray at around 12:30 h. Trend of both energy and exergy efficiency is similar except the magnitude. Maximum efficiency observed to be 83% and 16.5% for energy and exergy, respectively. Full article

(This article belongs to the Proceedings of The 4th International Electronic Conference on Entropy and Its Applications)

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