Special Issue "Symmetry and Entropy"

Managing Editor
Dr. Shu-Kun Lin
MDPI, Kandererstrasse 25, CH-4057 Basel, Switzerland
Website: http://www.mdpi.org/lin/
E-Mail:
Interests: molecular recognition; entropy; Gibbs paradox; irreversibility; stability; symmetry; similarity; diversity; diversity preservation; evolution; information theory; thermodynamics; enzyme inhibitors; heterocycles; isotopically-labeled compounds; Lewis acids and bases; quninoxaline N-oxides; photochemistry ESR; aromaticity; protein folding; nature of chemical processes

Guest Editor
Dr. Joe Rosen
Adjunct Professor, The George Washington University, Washington DC, USA
E-Mail:
Interests: symmetry; Curie principle; space; time; spacetime; quantum

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

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

Type of Paper: Communicaition
Title: Dispersal (Entropy) and Recognition (Information) as Foundations of Emergence and Submergence
Author: Bernard Testa
Affiliation: University Hospital Centre, 46 Rue du Bugnon, CH-1011 Lausanne – CHUV, Switzerland; E-Mail: Bernard.Testa@chuv.ch
Abstract: The objective of this writing is to reflect on a possible relation between entropy and emergence. A qualitative, relational approach is followed. We begin by highlighting that entropy includes the concept of dispersal relevant to our enquiry. Emergence in complex systems arises from the coordinated behaviour of their parts. Coordination in turn implies mutual recognition between parts, i.e., information exchange. What will be argued here is that the scope and efficiency of recognition processes between parts is improved when preceded by their dispersal, which multiplies the number and variety of encounters and creates a richer potential for recognition. A process intrinsic to emergence is submergence (aka dissolvence or top-down constraints), which participates in the information-entropy interplay underlying the creation and breakdown of higher-level entities.

Type of Paper: Article
Title: On the Evolution of Topological Entropy along Ricci Flow
Author: Pablo Suárez-Serrato; E-mail: p.suarez-serrato@cantab.net
Abstract: We show how recent results about surfaces can be used to provide examples of higher dimensional manifolds for which the topological entropy of the geodesic flow is:
1) Positive and decreases along the Ricci flow
2) Zero and increases along the Ricci flow