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Symmetry and Entropy

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 December 2009) | Viewed by 45903

Special Issue Editor

MDPI, St. Alban-Anlage 66, CH-4052 Basel, Switzerland
Interests: gibbs paradox; entropy; symmetry; similarity; diversity; information theory; thermodynamics; process irreversibility or spontaneity; stability; nature of the chemical processes; molecular recognition; open access journals

Special Issue Information

Dear Colleagues,

The relation between symmetry and entropy is a deep one. For isolated systems that are meaningfully describable in terms of microstates and macrostates, entropy S obeys the second law of thermodynamics and never decreases as the system evolves. A macrostate of such a system possesses a natural symmetry, its invariance under permutations of the set of microstates corresponding to it. Macroevolution is generally convergent, with the same final macrostate resulting from (usually many) different initial macrostates. But microevolution is nonconvergent, where different microstates always evolve into different microstates. (Nonconvergence is related to time reversal symmetry.) With the degree of symmetry of a macrostate represented by the number of its corresponding microstates W (monotonically related to the order of the symmetry group W!), it follows from the Curie principle (or symmetry principle) that the degree of symmetry of a macrostate never decreases as the system evolves. This is the special symmetry evolution principle and it is isomorphic with the second law under interchange of S and W. These two quantities are indeed monotonically increasing functions of each other through the famous relation S = k log W. This special issue celebrates that relation.

Dr. Shu-Kun Lin
Managing Editor

Keywords

  • Curie-Rosen symmetry principle (or Curie symmetry principle, or symmetry principle)
  • causality
  • symmetry evolution
  • continuous symmetry
  • similarity
  • indistinguishanbility
  • chirality
  • asymmetry

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Published Papers (5 papers)

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181 KiB  
Article
Particle Indistinguishability Symmetry within a Field Theory. Entropic Effects
by Dung Di Caprio and Jean Pierre Badiali
Entropy 2009, 11(2), 238-248; https://doi.org/10.3390/e11020238 - 21 Apr 2009
Cited by 3 | Viewed by 8642
Abstract
In this paper, we briefly discuss a field theory approach of classical statistical mechanics. We show how an essentially entropic functional accounts for fundamental symmetries related to quantum mechanical properties which hold out in the classical limit of the quantum description. Within this [...] Read more.
In this paper, we briefly discuss a field theory approach of classical statistical mechanics. We show how an essentially entropic functional accounts for fundamental symmetries related to quantum mechanical properties which hold out in the classical limit of the quantum description. Within this framework, energetic and entropic properties are treated at equal level. Based on a series of examples on electrolytes, we illustrate how this framework gives simple interpretations where entropic fluctuations of anions and cations compete with the energetic properties related to the interaction potential. Full article
(This article belongs to the Special Issue Symmetry and Entropy)
544 KiB  
Article
stu Black Holes Unveiled
by Stefano Bellucci, Sergio Ferrara, Alessio Marrani and Armen Yeranyan
Entropy 2008, 10(4), 507-555; https://doi.org/10.3390/e10040507 - 17 Oct 2008
Cited by 86 | Viewed by 10175
Abstract
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in [...] Read more.
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in d = 4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given. Full article
(This article belongs to the Special Issue Symmetry and Entropy)
183 KiB  
Article
An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory
by Joel Ratsaby
Entropy 2008, 10(1), 6-14; https://doi.org/10.3390/entropy-e10010006 - 20 Mar 2008
Cited by 12 | Viewed by 9864
Abstract
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering entity which introduces local disruption [...] Read more.
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering entity which introduces local disruption in randomness. This is modeled by a selection rule R which selects a subsequence of the random input sequence that hits the structure. Through the inequality that relates stochasticity and chaoticity of random binary sequences we maintain that Lin’s notion of stability corresponds to the stability of the frequency of 1s in the selected subsequence. This explains why more complex static structures are less stable. Lin’s third law is represented as the inevitable change that static structure undergo towards conforming to the universe’s perfect randomness. Full article
(This article belongs to the Special Issue Symmetry and Entropy)
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27 KiB  
Book Review
Symmetry Rules: How Science and Nature Are Founded on Symmetry. By Joe Rosen. Springer: Berlin. 2008, XIV, 305 p. 86 illus., Hardcover. CHF 70. ISBN: 978-3-540-75972-0
by Shu-Kun Lin
Entropy 2008, 10(2), 55-57; https://doi.org/10.3390/entropy-e10020055 - 16 Jun 2008
Cited by 1 | Viewed by 5914
Abstract
This book belongs to the book series The Frontiers Collection, edited by A.C. Elitzur, M.P. Silverman, J. Tuszynski, R. Vaas and H.D. Zeh.[...] Full article
(This article belongs to the Special Issue Symmetry and Entropy)
47 KiB  
Commentary
The Symmetry Principle
by Joe Rosen
Entropy 2005, 7(4), 308-313; https://doi.org/10.3390/e7040308 - 15 Dec 2005
Cited by 18 | Viewed by 9139
Abstract
The symmetry principle is described in this paper. The full details are given in the book: J. Rosen, Symmetry in Science: An Introduction to the General Theory (Springer-Verlag, New York, 1995). Full article
(This article belongs to the Special Issue Symmetry and Entropy)
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