New thermodynamic fluctuation theory using path integrals

Abstract

The conventional thermodynamic fluctuation theory, originated by Einstein in 1907, fails at volumes less than the correlation volume because it does not include the effects of local correlations. In this paper, a new thermodynamic fluctuation theory is developed in which an attempt is made to include local correlations by considering successive fluctuations in a sequence of systems of decreasing volume. The mathematics used is a path-integral formalism developed recently primarily for application in irreversible thermodynamics. An important result of the new theory is that it predicts the correlation length in terms of purely thermodynamic quantities, confirming a conjecture made earlier by the author on the basis of a Riemannian geometric model of thermodynamics. There is also a possibility that this new theory works at volumes less than the correlation volume and, hence, that it provides a thermodynamic theory of critical fluctuations. Unfortunately, due to mathematical difficulties, this interesting possibility is not put to a direct test in this paper.