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Special Issue "Symmetry and Entropy"

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

Deadline for manuscript submissions: closed (31 December 2009)

Special Issue Editor

Managing Editor
Dr. Shu-Kun Lin

MDPI AG, St. Alban-Anlage 66, CH-4052 Basel, Switzerland
Website | E-Mail
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

Related Special Issue

Published Papers (5 papers)

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Research

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Open AccessArticle Particle Indistinguishability Symmetry within a Field Theory. Entropic Effects
Entropy 2009, 11(2), 238-248; doi:10.3390/e11020238
Received: 30 December 2008 / Accepted: 20 April 2009 / Published: 21 April 2009
PDF Full-text (181 KB)
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
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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)
Open AccessArticle stu Black Holes Unveiled
Entropy 2008, 10(4), 507-555; doi:10.3390/e10040507
Received: 5 October 2008 / Accepted: 13 October 2008 / Published: 17 October 2008
Cited by 66 | PDF Full-text (544 KB) | HTML Full-text | XML Full-text
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
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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)
Open AccessArticle An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory
Entropy 2008, 10(1), 6-14; doi:10.3390/entropy-e10010006
Received: 28 February 2008 / Revised: 16 March 2008 / Accepted: 19 March 2008 / Published: 20 March 2008
Cited by 8 | PDF Full-text (183 KB)
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
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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)

Other

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Open AccessBook 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
Entropy 2008, 10(2), 55-57; doi:10.3390/entropy-e10020055
Received: 14 April 2008 / Published: 16 June 2008
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(This article belongs to the Special Issue Symmetry and Entropy)
Open AccessCommentary The Symmetry Principle
Entropy 2005, 7(4), 308-313; doi:10.3390/e7040308
Received: 13 December 2005 / Accepted: 14 December 2005 / Published: 15 December 2005
Cited by 7 | PDF Full-text (47 KB) | HTML Full-text | XML Full-text
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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