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Special Issue "Entropy, Order and Symmetry"

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A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2009)

Special Issue Editors

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
Assistant Editor
Ms. Laura Simon

MDPI AG, St. Alban-Anlage 66, 4052 Basel, Switzerland
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Special Issue Information

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

Keywords

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

Related Special Issue

Published Papers (3 papers)

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Research

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Open AccessArticle Miscellania about Entropy, Energy, and Available Free Energy
Symmetry 2010, 2(2), 916-934; doi:10.3390/sym2020916
Received: 25 February 2010 / Revised: 12 April 2010 / Accepted: 14 April 2010 / Published: 19 April 2010
Cited by 1 | PDF Full-text (556 KB)
Abstract
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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy, Order and Symmetry)

Review

Jump to: Research

Open AccessReview Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics
Symmetry 2010, 2(3), 1201-1249; doi:10.3390/sym2031201
Received: 13 January 2010 / Revised: 9 June 2010 / Accepted: 21 June 2010 / Published: 24 June 2010
Cited by 10 | PDF Full-text (596 KB)
Abstract
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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Entropy, Order and Symmetry)
Open AccessReview Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Symmetry 2010, 2(2), 970-998; doi:10.3390/sym2020970
Received: 12 January 2010 / Revised: 13 April 2010 / Accepted: 21 April 2010 / Published: 29 April 2010
Cited by 2 | PDF Full-text (211 KB)
Abstract
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
[...] Read more.
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). Full article
(This article belongs to the Special Issue Entropy, Order and Symmetry)

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