Thermodynamic Bounds on Constant-Volume Heat Capacities and Adiabatic Compressibilities

Abstract

A rigorous upper bound for the heat capacity at constant volume $C_V$ is used to provide an alternative derivation of a result due to Rice: A locus of points of infinite $C_V$ is in general incompatible with thermodynamic stability. An analogous upper bound is obtained for the adiabatic compressibility. The bounds are extended to multicomponent stystems, where they suggest that $C_V$ should not diverge along a continuous line of critical points or plait points. They make plausible the absence of an infinite heat capacity in a certain class of "decorated" Ising models (including Syozi's model for a dilute ferromagnet) and in the spherical model. Possible implications for fluids or ferromagnets containing impurities are briefly discussed.