Pressure-dependent partition functions

It is shown that the partition functions relating to statistical ensembles can be classified as cumulative, distributive or differential with regard to any of the extensive thermodynamic variables. The Laplace transforms involved in the general formulation of transformed partition functions, when extensive parameters are replaced by their conjugate intensive variables, are two-sided and appear in different forms according to the classification mentioned. The petit partition function at constant pressure can be defined for both classical and quantal systems as a Stieltjes integral or dimensionless Laplace transform over the volume-dependent partition function. This expression contains no arbitrary external parameters and satisfies all the conditions formulated by Munster; it can be interpreted as the ratio of two partition functions, the one relating jointly to the system and a macroscopic boundary, and the second to the boundary alone. It is known that the constant pressure grand partition function as def...