The work is a brief review of articles by the author and his young colleagues to describe the classical statistical systems with the use of properties of integrals with respect to Poisson measure on configuration space. A variant of cell gas model which is an approximation of the continuous classical gas is proposed. Cell gas (CG) model for continuous classical system of interacting point particles is defined as follows. For a given partition [Formula: see text] of the space ℝd into an infinite set of mutually disjoint hypercubes with edges a, every point of a phase space of an infinite particle system is a configuration in which every hypercube [Formula: see text] contains no more than one particle. We present a structure of measurable sets of the configuration space and show that for strong superstable interaction the pressure and correlation functions of the system pointwise converge to the corresponding values of the conventional continuous system if the edges a of cubes [Formula: see text] tend to zero. We also define lattice gas (LG) model which approximates the CG model and thus provides a continuous transition LG model in the model of continuous gas.
A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of classical statistical mechanics. We define some kind of approximation of main quantities, which describe macroscopical and microscopical characteristics of systems, such as grand partition function and correlation functions. The pressure of an approximated system converges to the pressure of the initial system if the parameter of approximation a→0 for any values of an inverse temperature β>0 and a chemical activity z. The same result is true for the family of correlation functions in the region of small z.
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