On the negative specific heat paradox

Abstract

Conditions under which self-gravitating systems naturally have negative specific heats are outlined, and an exactly calculable self-gravitating model is presented. The reasons why a system in stable thermodynamic equilibrium cannot have a negative specific heat if it is either extensive or in contact with a heat bath are reviewed. It is shown that large-scale attractive forces cause negative specific heats in a microcanonical ensemble and a giant phase transition in a canonical ensemble. The question of whether all normal phase transitions may not be generated by negative-specific-heat elements at a microscopic level is investigated by considering a simple model of a chemical dissociation. The microscopic negative-specific-heat elements that cause the transition are isolated.