http://www.mdpi.com/journal/symmetry/special_issues/entropy-symmetry/ Dear Colleagues, As a chemist, I have been trying very hard to set up an axiomatic formula of symmetry, order, entropy and stability. The task is truly very big and my efforts stirred up more problems than it appeared to have solved. This is the main reason that I am motivated to launch the journals Entropy (http://www.mdpi.com/journal/entropy/), Symmetry (http://www.mdpi.com/journal/symmetry/) together with several scientists, see the editorials at http://www.mdpi.com/1099-4300/1/1/1/pdf/ and http://www.mdpi.com/2073-8994/1/1/1/pdf/. I sincerely welcome you to contribute your paper and bring some progress to the studies of this topic. Dr. Shu-Kun Lin Managing Editor Related Special Issues in other Journals Symmetry and Entropy in Entropy Submission Information All papers should be submitted to symmetry@mdpi.com. To be published continuously until the deadline and papers will be listed together at the special issue website. Submitted papers should not have been published nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors is available on the Instructions for Authors page. Symmetry is a new international, peer-reviewed, quarterly open access journal published by MDPI. Open Access publication is free of charge for manuscripts submitted in 2009 and published in the first few issues od Symmetry. English correction fees and/or formatting fees of 250 CHF will be billed in certain cases (250 CHF per paper for those papers that require extensive additional formatting and/or English corrections). http://www.mdpi.com/2073-8994/2/3/1201/ A detailed analysis of deterministic (one-to-one) and stochastic (one-to-many) dynamics establishes that dS/dt > 0 is only consistent with the latter, which contains violation of temporal symmetry and homogeneity. We observe that the former only supports dS/dt = 0 and cannot give rise to Boltzmann’s molecular chaos assumption. The ensemble average is more meaningful than the temporal average, especially in non-equilibrium statistical mechanics of systems confined to disjoint phase space components, which commonly occurs at low temperatures. We propose that the stochasticity arises from extra degrees of freedom, which are not part of the system. We provide a simple resolution of the recurrence and irreversibility paradoxes. http://www.mdpi.com/2073-8994/2/3/1201/ Thu, 24 Jun 2010 00:00:00 CEST Symmetry 2010-06-24 2 3 Review 1201 1249 2073-8994 Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics 2010-06-24 doi: 10.3390/sym2031201 Gujrati http://www.mdpi.com/2073-8994/2/2/970/ We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections). http://www.mdpi.com/2073-8994/2/2/970/ Thu, 29 Apr 2010 00:00:00 CEST Symmetry 2010-04-29 2 2 Review 970 998 2073-8994 Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics 2010-04-29 doi: 10.3390/sym2020970 Fatibene Francaviglia Mercadante http://www.mdpi.com/2073-8994/2/2/916/ While the main concepts of thermodynamics are universal, the application to specific systems is not. Thus, the universal concepts combined with specific constitutive relations permit the derivation of important results in such fields as diverse as physics, chemistry, physical chemistry, chemical engineering and rheology. In all of these fields equilibrium is characterized either by a maximum of entropy or by a minimum of available free energies, depending on boundary data. In the latter case there is a compromise between the entropic tendency to grow and the energetic tendency to decrease. After some historical considerations the situation is illustrated for several specific cases: planetary atmospheres, osmosis and elastic rubber molecules, pertaining to physics, chemistry and rheology respectively. Afterwards, in the later parts of the article, thermodynamics considerations are extrapolated to remote fields, to wit evolutionary genetics and sociology. http://www.mdpi.com/2073-8994/2/2/916/ Mon, 19 Apr 2010 00:00:00 CEST Symmetry 2010-04-19 2 2 Article 916 934 2073-8994 Miscellania about Entropy, Energy, and Available Free Energy 2010-04-19 doi: 10.3390/sym2020916 Müller