Cell gas model of classical statistical systems (Q2846888)

This article reviews the recent results of the author and his coworkers mentioned in the list of references. The aim is to work out a theory of classical statistical systems based on Poisson measures in configuration spaces and so the foundation of a more comprehensive statistical theory. The starting proposal is to find a variant of cell gas model which is an approximation of the continuous classical gas, a system of interacting point particles. For a given partition in this space there corresponds an infinite set of mutually disjoint hypercubes with edges \(\underline a\), so that every hypercube contains at most one particle. The structure of measurable sets of the configuration space is presented and it is shown that for strong superstable interaction (defined rigorously) the pressure and the correlation functions of the system converge to the corresponding values of the conventional continuous physical system if the parameter \(\underline a\) tends to zero. A lattice gas model, too, is defined which approximates the cell gas model and this realizes a continuous transition of this model to the model of continuous gas.NEWLINENEWLINE The main results may be formulated as follows: For superstable point particles which interact among others the physical properties and thermodynamic functions of the classical system can be approximated with any pre-specified accuracy.