Reply to the Comment by D. Lynden-Bell and R. M. Lynden-Bell

Abstract

Lynden-Bell and Lynden-Bell (LBLB) [1] conclude that the arguments advanced in our letter [2] concerning the impossibility of negative heat capacities in nanoclusters do not apply universally, and argue that negative heat capacities do occur in inhomogeneous systems. They present a simple model of an inhomogeneous system and arguments concerning a stability criterion, both of which, they claim, admit negative heat capacity. Here, we analyze their model and arguments and show that they contain physical inconsistencies and therefore are not representative of real systems in thermodynamic equilibrium. Our letter [2] argues that a real system in thermodynamic equilibrium, or any model purporting to represent such a system, must have a positive definite heat capacity. It is important to distinguish between such a real system and a model system lacking physical consistency, and between a system in thermodynamic equilibrium and a system in a metastable state. A system in thermodynamic equilibrium is in a unique, globally stable, state of maximum entropy that is independent of the initial conditions [3]. This state is thermically, chemically and mechanically stable, and thus, if there are no external fields, the intensive variables of the system are macroscopically homogeneous [4]. The phase space volume of such a system in thermodynamic equilibrium can increase at most as a power law with energy, with the exponent of the power law being proportional to the dimensionality of the state space. Application of equilibrium thermodynamic formalism to this system leads to consistent results within the formalism; for example, that the heat capacity at constant volume and particle number, or constant pressure and particle number, are positive definite quantities.