Abstract
A systematic development is given of the view that in the case of systems with long-range forces and which are therefore nonextensive (in some sense) some thermodynamic results do not hold. Among these is the relationU − TS + pΝ = ΜN and the Gibbs-Duhem equation. If a search for an equilibrium state is made by maximization of the entropy one may obtain misleading results because superadditivity may be violated. The considerations are worked out for a simple gas model, but they are relevant to black hole thermodynamics. Rather general conclusions can be drawn which transcend special systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. T. Landsberg and D. Tranah, Thermodynamics of non-extensive entropies I,Collec. Phenom. 3:73–80 (1980).
D. Tranah and P. T. Landsberg, Thermodynamics of non-extensive entropies II,Collect. Phenom. 3:81–88 (1980).
P. T. Landsberg and D. Tranah, Entropies need not be concave,Phys. Lett. 78A:219–220 (1980).
J. Dunning-Davies, On the meaning of extensivity,Phys. Lett. 94A:346–348 (1983).
P. T. Landsberg,Thermodynamics with Quantum Statistical Illustrations (Wiley, New York, 1961).
P. T. Landsberg, The fourth law of thermodynamics (book review),Nature 238:229–231 (1972).
P. G. Wright, Chemical thermodynamics in Landsberg's formulation,Proc. R. Soc. London Ser. A 317:477–510 (1970).
J. Kestin, book review,Amer. Sci. 68:230 (1980).
L. Galgani and A. Scotti,Proceedings of the International Conference on Thermodynamics, Cardiff, 1970, P. T. Landsberg, ed., pp. 229–235; also inPure Appl. Chem. 22:229–235 (1970).
P. T. Landsberg, Main ideas in the axiomatics of thermodynamics, in Proceedings of the International Conference on Thermodynamics, Cardiff, 1970, P. T. Landsberg, ed., pp. 215–277; also inPure Appl. Chem. 22:229–235 (1970).
W. Thirring,Lehrbuch der Mathematischen Physik, Vol. IV (Springer, Vienna, 1980).
A. Pflug,Commun. Math. Phys. 78:83 (1980).
R. Carlitz,Phys. Rev. D 5:3231 (1972).
T. Celik and H. Satz,Z. Phys. C1:163 (1979).
J. Messer,Phys. Lett. A83:304 (1981).
Author information
Authors and Affiliations
Additional information
Based on a seminar given at the University of Florida, April 1983.
On leave of absence from the Faculty of Mathematical Studies, University, Southampton S09 5NH, England.
Rights and permissions
About this article
Cite this article
Landsberg, P.T. Is equilibrium always an entropy maximum?. J Stat Phys 35, 159–169 (1984). https://doi.org/10.1007/BF01017372
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01017372