Length Scale for the Constant Pressure Ensemble: Application to Small Systems and Relation to Einstein Fluctuation Theory

Abstract

In this paper we address the constant pressure ensemble and the volume scale that must be introduced in order to represent the corresponding partition function as a dimensionless integral. The volume scale or length scale problem arises quite generally when it is necessary (for whatever reason) to apply semiclassical statistical mechanical theory in configuration space alone, rather than in the full phase space of the system. We find that the length scale, derived by earlier workers concerned primarily with systems in the thermodynamic limit, is not suitable for application of the constant pressure ensemble to small systems such as clusters in nucleation theory or mesodomains in microemulsion theory. We discuss some of the well-known deficiencies of the conventional representation of the constant pressure ensemble and some which are not so well-known. Also the close connection between the constant pressure ensemble and Einstein fluctuation theory is emphasized, and we clarify the two types of fluctuation ...