Summary
« Natural » properties lead to a representation theorem for the entropy functional of a grand canonical ensemble. In addition to the classical Boltzmann term, the representation contains three more terms that seem to be meaningful in statistical mechanics.
Sunto
Da proprietà « naturali » imposte al funzionale entropia di un insieme gran canonico si deduce un teorema di rappresentazione per esso. In aggiunta al termine classico di Boltzmann, la rappresentazione mette in luce tre ulteriori termini che sembrano significativi in meccanica statistica.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. W. Robinson —D. Ruelle,Mean entropy of states in classical statistical mechanics, Commun. Math. Phys.,5 (1967), pp. 288–300.
E. H. Lieb,Some convexity and subadditivity properties of entropy, Bull. Amer. Math. Soc.,81, no. 1 (1975), pp. 1–13.
J. Aczél —B. Forte —C. T. Ng,Why the Shannon and Hartley entropies are « natural », Adv. Appl. Prob.6 (1974), pp. 131–146.
B. Forte —C. C. A. Sastri,Is something missing in the Boltzmann entropy?, Journal of Math. Phys.,16, no. 7 (1975), pp. 1453–1456.
M. Kuczma,Convex Functions, C.I.M.E., III ciclo, ed. Cremonese, Roma (1971), pp. 195–213.
Author information
Authors and Affiliations
Additional information
A Dario Graffi per il suo 70° compleanno
Entrata in Redazione il 17 marzo 1976.
While on sabbatical leave of absence from the University of Waterloo, Canada, Department of Applied Mathematics.
Research supported in part by National Research Council of Canada, grant A-7677 and IBM-Italia.
Rights and permissions
About this article
Cite this article
Forte, B. A characterization of the entropy functionals for grand canonical ensembles. The discrete case. Annali di Matematica 111, 213–228 (1976). https://doi.org/10.1007/BF02411820
Issue Date:
DOI: https://doi.org/10.1007/BF02411820