Abstract
Under the assumption of an identity determining the free energy of a state of a statistical mechanical system relative to a given equilibrium state by means of the relative entropy, it is shown: first, that there is in any physically definable convex set of states a unique state of minimum free energy measured relative to a given equilibrium state; second, that if a state has finite free energy relative to an equilibrium state, then the set of its time translates is a weakly relatively compact set; and third, that a unique perturbed equilibrium state exists following a change in Hamiltonian that is bounded below.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. J. Donald,Commun. Math. Phys. 105:13 (1986).
O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics, Vol. II (Springer-Verlag, New York, 1981).
M. J. Donald,Math. Proc. Camb. Phil. Soc. 101:363 (1987).
H. Araki,Commun. Math. Phys. 44:1 (1975).
D. Petz,Commun. Math. Phys. 105:123 (1986).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Volume III,Scattering Theory (Academic Press, New York, 1979).
H. Araki,Publ. Res. Inst. Math. Sci. (Kyoto) 9:165 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Donald, M.J. Free energy and the relative entropy. J Stat Phys 49, 81–87 (1987). https://doi.org/10.1007/BF01009955
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01009955