Classical fluids of negative heat capacity

Abstract

It is shown that new parametersX can be defined such that the heat capacity C_x≡T(∂S/∂T)_x is negative, even when the canonical ensemble [i.e., at fixed T=(∂U/∂S)_Y and Y≠X] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular κ_T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes C_x<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed.