Correlation Functionals

Abstract

The correlations between positions of particles in classical equilibrium statistical mechanics are usually expressed by correlation functions. It can be seen that if the correlation functions of a system are known, its configurational entropy per unit volume is already determined (independently of the interaction potential or other thermodynamical parameters). In this paper we consider all sequences of functions of an increasing number of variables (these functions are candidates for correlation functions) for which an entropy per unit volume may be defined. These sequences are called correlation functionals and are investigated in detail. They prove useful to the study of the limit of an infinite system in statistical mechanics (thermodynamic limit). Furthermore they allow the segregation of certain thermodynamic systems into phases to be made evident.