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Entropy, Volume 11, Issue 1 (March 2009), Pages 1-221

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Editorial

Jump to: Research, Review

Open AccessEditorial Entropy – New Editor-in-Chief and Outlook
Entropy 2009, 11(1), 1-3; doi:10.3390/e11010001
Received: 27 December 2008 / Published: 28 December 2008
PDF Full-text (156 KB)
Open AccessEditorial Concepts of Entropy and Their Applications
Entropy 2009, 11(1), 59-61; doi:10.3390/e11010059
Received: 8 February 2009 / Accepted: 9 February 2009 / Published: 12 February 2009
Cited by 1 | PDF Full-text (111 KB)
Abstract
Since a connection was made in the 19th Century between increase of entropy and earlier expressions of the Second Law of Thermodynamics, the topic has continued to fascinate engineers, physicists, chemists, computer scientists, mathematicians and philosophers. The topic of entropy is very [...] Read more.
Since a connection was made in the 19th Century between increase of entropy and earlier expressions of the Second Law of Thermodynamics, the topic has continued to fascinate engineers, physicists, chemists, computer scientists, mathematicians and philosophers. The topic of entropy is very much alive, as witnessed by the highly cited proceedings of a lively conference on the subject, held in Dresden Germany in 2000 [1]. Our intention in running a theme program seven years after the Dresden conference was to stimulate connections between entropy theory and broader applications. The papers in this special issue arose from a meeting of the AMSI-MASCOS Theme Program, Concepts of Entropy and their Applications, which took place in Melbourne Australia, November 26- December 12, 2007. [...] Full article

Research

Jump to: Editorial, Review

Open AccessArticle Viscoelastic Effects on the Entropy Production in Oscillatory Flow between Parallel Plates with Convective Cooling
Entropy 2009, 11(1), 4-16; doi:10.3390/e11010004
Received: 13 November 2008 / Accepted: 22 December 2008 / Published: 28 December 2008
Cited by 5 | PDF Full-text (478 KB)
Abstract
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. With these conditions, the amount of heat entering or leaving the system depends on the external [...] Read more.
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. With these conditions, the amount of heat entering or leaving the system depends on the external temperature as well as on the convective heat transfer coefficient. 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. For a discrete set of values of the oscillatory Reynolds number, the extracted heat from one of the plates shows maxima. Full article
Open AccessArticle The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields
Entropy 2009, 11(1), 17-31; doi:10.3390/e11010017
Received: 11 June 2008 / Accepted: 11 January 2009 / Published: 23 January 2009
Cited by 4 | PDF Full-text (320 KB)
Abstract
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of [...] Read more.
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent ’particle’ description fails, and the wave nature becomes apparent. Full article
Open AccessArticle Information, Deformed қ-Wehrl Entropies and Semiclassical Delocalization
Entropy 2009, 11(1), 32-41; doi:10.3390/e11010032
Received: 5 November 2008 / Accepted: 20 January 2009 / Published: 27 January 2009
Cited by 4 | PDF Full-text (221 KB)
Abstract
Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the [...] Read more.
Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associatedWehrl entropies, suitably қ-deformed. We are able to show that it is possible to significantly improve on the extant phase-space classical-localization power. Full article
(This article belongs to the Special Issue Information and Entropy)
Open AccessArticle Euclidean Quantum Mechanics and Universal Nonlinear Filtering
Entropy 2009, 11(1), 42-58; doi:10.3390/e11010042
Received: 1 January 2009 / Accepted: 6 February 2009 / Published: 12 February 2009
Cited by 7 | PDF Full-text (250 KB)
Abstract
An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. [...] Read more.
An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation. Full article
Open AccessArticle Structural Entropy to Characterize Small Proteins (70 aa) and Their Interactions
Entropy 2009, 11(1), 62-84; doi:10.3390/e11010062
Received: 26 November 2008 / Accepted: 19 February 2009 / Published: 20 February 2009
Cited by 3 | PDF Full-text (1035 KB)
Abstract
Proteins composed of short polypeptide chains (about 70 amino acid residues) participating in ligand-protein and protein-protein (small size) complex creation were analyzed and classified according to the hydrophobicity deficiency/excess distribution as a measure of structural and functional specificity and similarity. The characterization [...] Read more.
Proteins composed of short polypeptide chains (about 70 amino acid residues) participating in ligand-protein and protein-protein (small size) complex creation were analyzed and classified according to the hydrophobicity deficiency/excess distribution as a measure of structural and functional specificity and similarity. The characterization of this group of proteins is the introductory part to the analysis of the so called `Never Born Proteins' (NBPs) in search of protein compounds of biological activity in pharmacological context. The entropy scale (classification between random and deterministic limits) estimated according to the hydrophobicity irregularity organized in ranking list allows the comparative analysis of proteins under consideration. The comparison of the hydrophobicity deficiency/excess appeared to be useful for similarity recognition, examples of which are shown in the paper. The influence of mutations on structure and hydrophobicity distribution is discussed in detail. Full article
Figures

Open AccessArticle Generalized Complexity and Classical-Quantum Transition
Entropy 2009, 11(1), 111-123; doi:10.3390/e11010111
Received: 10 January 2009 / Accepted: 26 February 2009 / Published: 4 March 2009
Cited by 5 | PDF Full-text (362 KB)
Abstract
We investigate the classical limit of the dynamics of a semiclassical system that represents the interaction between matter and a given field. On using as a quantifier the q- Complexity, we find that it describes appropriately the quantum-classical transition, detecting the most [...] Read more.
We investigate the classical limit of the dynamics of a semiclassical system that represents the interaction between matter and a given field. On using as a quantifier the q- Complexity, we find that it describes appropriately the quantum-classical transition, detecting the most salient details of the changeover. Additionally the q-Complexity results a better quantifier of the problem than the q-entropy, in the sense that the q-range is enlarged, describing the q-Complexity, the most important characteristics of the transition for all q-value. Full article
Open AccessArticle Thermodynamics of High Temperature Plasmas
Entropy 2009, 11(1), 124-221; doi:10.3390/e11010124
Received: 19 December 2008 / Accepted: 4 March 2009 / Published: 13 March 2009
Cited by 2 | PDF Full-text (991 KB) | Correction | Supplementary Files
Abstract
In this work we discuss how and to what extent the thermodynamic concepts and the thermodynamic formalism can be extended to the description of high temperature states of the plasma not necessarily associated with a Boltzmann distribution and with thermal equilibrium.The discussion [...] Read more.
In this work we discuss how and to what extent the thermodynamic concepts and the thermodynamic formalism can be extended to the description of high temperature states of the plasma not necessarily associated with a Boltzmann distribution and with thermal equilibrium.The discussion is based on the “magnetic or electrostatic entropy concept”, an interpretative and predictive tool based on probability and information, defined in a suitably coarse-grained possibility space of all current density or of all electric charge density distributions under testable constraints, and whose variation properties are proven to be related under certain conditions to the equilibrium and the stability of the system. In the case of magnetic equilibrium the potentiality of the magnetic entropy concept is illustrated by comparing the predictions of the current density and pressure profiles with the observations in different tokamak machines and different tokamak regimes, as well as by showing how the equilibrium and the stability in devices as different as the reversed field pinch or the magnetic well are described by the variation properties of the same entropy functional applied to the different situations. In fact it emerges that the maximum of the entropy can be seen in these different cases as an optimization constraint for the minimum of the magnetic energy. The application of the entropy concept to the electrostatic processes shows in particular that the so-called reactive instabilities (non-dissipative, non-resonant instabilities with a marginal point) admit a neighboring state with higher entropy and are therefore of special relevance from the point of view of the physical evolution of the system. In this case the thermodynamic formalism allows the introduction of the concept of “thermodynamic fluctuations” of the macroscopic charge density and provides a method for the calculation of the “thermodynamic” fluctuation levels both on the stable as well as on the linearly unstable side of the marginal point. The paper discusses the relation between the variations of the entropy functional defined on statistical grounds and the motion of the underlying system of particles. It is found that the vanishing of the first variation of the entropy is connected, under certain assumptions, with the Hamilton’s principle, while the second variation is not directly related to the dynamics but is an expression of the fact that the entropy is a predictive tool based on probability and information. Full article

Review

Jump to: Editorial, Research

Open AccessReview The Insights of Algorithmic Entropy
Entropy 2009, 11(1), 85-110; doi:10.3390/e11010085
Received: 18 November 2008 / Accepted: 20 January 2009 / Published: 4 March 2009
Cited by 8 | PDF Full-text (410 KB)
Abstract
The algorithmic entropy of a system, the length of the shortest algorithm that specifies the system’s exact state adds some missing pieces to the entropy jigsaw. Because the approach embodies the traditional entropies as a special case, problematic issues such as the [...] Read more.
The algorithmic entropy of a system, the length of the shortest algorithm that specifies the system’s exact state adds some missing pieces to the entropy jigsaw. Because the approach embodies the traditional entropies as a special case, problematic issues such as the coarse graining framework of the Gibbs’ entropy manifest themselves in a different and more manageable form, appearing as the description of the system and the choice of the universal computing machine. The provisional algorithmic entropy combines the best information about the state of the system together with any underlying uncertainty; the latter represents the Shannon entropy. The algorithmic approach also specifies structure that the traditional entropies take as given. Furthermore, algorithmic entropy provides insights into how a system can maintain itself off equilibrium, leading to Ashby’s law of requisite variety. This review shows how the algorithmic approach can provide insights into real world systems, by outlining recent work on how replicating structures that generate order can evolve to maintain a system far from equilibrium. Full article

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