The Concavity of Entropy and Extremum Principles in Thermodynamics

Journal of Statistical Physics

Volumn 111, Issue 1-2, 2003, Pages 479-493

  Prestipino, Santi ^a   Giaquinta, Paolo V ^a  

^a UNIVERSITY OF MESSINA   (Italy)

Author keywords

Entropy concavity; Equilibrium thermodynamics; Maximum entropy principle; Thermodynamic representation theory

Indexed keywords

EID: 0037279147     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022233814184     Document Type: Article

References (5)

1. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, 1985).
2. An expanded version of the present article, containing two appendices with some useful technical material, is available at http://www.me.infm.it/̃prestip. In particular, Appendix A of the web version summarizes some properties of concave (and convex) functions that are used in the following, while Appendix B collects a number of relevant results concerning Legendre transforms and their derivatives.
3. 2 > 0.
4. Alternatively, one can define F̃ as U(S, V) - TS. In this case, F̃ would be a function of S which parametrically depends on T and V. Anyway, the minimum and the convexity properties of F̃ remain the same (see Appendix B of ref. 2).
5. See, for instance, I. Ispolatov and E. G. D. Cohen, On first-order phase transitions in microcanonical and canonical non-extensive systems, Physica A 295:475-487 (2001).