Abstract

The present work extends the well-known thermodynamic relation C = ß2 for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity = 1 + ?2S(E)/ ?E2 can account for thermodynamic states with a negative heat capacity C < 0; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve ß(E) = ?S(E)/?E. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics. © 2009 IOP Publishing Ltd.