Abstract:
A classical lattice system is defined as a system consisting of a large number of classical subsystems (lattice sites) that, depending on the position on the lattice, can interact in some manner with each other. A hierarchy of BBGKY equations is obtained for describing the evolution of the probability densities (normalized to unity) which determine the state of the classical lattice system. A one-dimensional system of classical particles interacting through a finite-range potential with hard core is interpreted as a classical lattice system.
A formula is found for solving the BBGKY equations for such a system. A mathematical structure in which this formula has mathematical significance is found. To the states of the system there correspond countably additive measures on the phase space of an infinite number of particles.
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