Contributions to Statistical Mechanics Far from Equilibrium. IV: Improved and Simplified Treatment of Non-Steady States

Abstract

The method of dealing with non-steady states presented in Part II of this series is improved and simplified by dissociation of the reference Gaussian distribution function from local equilibrium states. Furthermore, a new approach gives an extra degree of freedom of choosing the variance of the reference distribution function, and its advantage is briefly dis­ cussed with an illustrative example. § 1. Introductioh In Part II of this series of papers 1l devoted to statistical mechanics far from equilibrium we have presented a method for obtaining the probability distribution function of gross variables in a non-steady situation. Since then have arisen some circumstances that necessitate improvement and further extension of the methpd. (1) The method of II begins with the local equilibrium distribution function of a Gaussian form but this is not always adequate. For instance, if the process under consideration starts from a thermodynamically unst~ble state (spinodal decomposition2l) or passes through such a state (nucleation 3l), the variance of the Gaussian local equilibrium distribution blows up. (2) With the method of II the Gaussian local equilibrium distribution . furictiqn is implicitly assumed to be also formed by application of an external field and hence II (2 · 8) is assumed for the Gaussian local equilibrium distribution g10 (t). This, however, has the effect of restricting the theory to the cases where the variance of the local equilibrium distribution does not vary in time. Hence the part of II dealing with the cases where the variance changes in time is incomplete and unnecessarily complicated. In the present paper we present a modified version of II by dissociating the starting reference Gaussian distribution function from local equilibrium states. This leaves some. arbitrariness in the formalism which can be fixed later on to our best advantage. Many of the developments of II are still applicable to a