http://www.mdpi.com/journal/entropy/special_issues/symmetry_entropy/ Dr. Joe Rosen's Introduction for special issue “Symmetry and Entropy” 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. Joe Rosen 20 February 2008 Related Special Issues in other Journals Entropy, Order and Symmetry in Symmetry Submission All papers should be submitted to entropy@mdpi.org with copy to the guest editor. To be published continuously until the deadline and papers will be listed together at the special websites. Both, research articles and review articles are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editors for announcment on this website. Submitted papers should not have been published previously, nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors, sample copies and other relevant information for submitting papers are available on the Instructions for Authors page. Entropy is an international peer-reviewed quarterly journal published by Molecular Diversity Preservation International. Please visit the Instructions for Authors page before submitting a paper. Open Access publication fees are 800 CHF per paper. English correction fees (250 CHF) will be added in certain cases (1050 CHF per paper for those papers that require extensive additional formatting and/or English corrections.). http://www.mdpi.com/1099-4300/11/2/238/ 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. http://www.mdpi.com/1099-4300/11/2/238/ Tue, 21 Apr 2009 00:00:00 CEST Entropy 2009-04-21 11 2 Article 238 248 1099-4300 Particle Indistinguishability Symmetry within a Field Theory. Entropic Effects 2009-04-21 doi: 10.3390/e11020238 Dung di Caprio Jean Pierre Badiali http://www.mdpi.com/1099-4300/10/4/507/ 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. http://www.mdpi.com/1099-4300/10/4/507/ Fri, 17 Oct 2008 00:00:00 CEST Entropy 2008-10-17 10 4 Article 507 555 1099-4300 stu Black Holes Unveiled 2008-10-17 doi: 10.3390/e10040507 Stefano Bellucci Sergio Ferrara Alessio Marrani Armen Yeranyan http://www.mdpi.com/1099-4300/10/2/55/ n/a http://www.mdpi.com/1099-4300/10/2/55/ Mon, 16 Jun 2008 00:00:00 CEST Entropy 2008-06-16 10 2 Book Review 55 57 1099-4300 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 2008-06-16 doi: 10.3390/entropy-e10020055 Shu-Kun Lin http://www.mdpi.com/1099-4300/10/1/6/ 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. http://www.mdpi.com/1099-4300/10/1/6/ Thu, 20 Mar 2008 00:00:00 CET Entropy 2008-03-20 10 1 Article 6 14 1099-4300 An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory 2008-03-20 doi: 10.3390/entropy-e10010006 Joel Ratsaby http://www.mdpi.com/1099-4300/7/4/308/ 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). http://www.mdpi.com/1099-4300/7/4/308/ Thu, 15 Dec 2005 00:00:00 CET Entropy 2005-12-15 7 4 Commentary 308 313 1099-4300 The Symmetry Principle 2005-12-15 doi: 10.3390/e7040308 Joe Rosen