Abstract
Abstract The statistical evolution of a classical system of N particles with pair interactions can in principle be studied by means of the BBGKY hierarchy for the reduced distribution functions. If no approximation is made, the evolution equation of the one-particle distribution function involves the two-particle distribution function, and so on. The study of the evolution of the one-particle distribution function is thus tricky. However, in some cases, it is possible, through proper approximations, to obtain a closed evolution equation for this distribution function. If the effect of collisions leading to an irreversible evolution is taken into account by these approximations, the evolution equation thus obtained for the one-particle distribution function belongs to the class of kinetic equations. There are several types of such equations, each of them relating to a particular physical system placed in given conditions.
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