The principle of maximum entropy and Boltzmann type kinetic equations (Q1099902)

The problem of the paper is the possibility of a dynamical justification of the principle of maximum entropy in the sense of a dynamical semigroup of open systems. It has been shown that, under the assumption of a convex dynamical semigroup defined on discrete and finite probability distributions (a finite sample space), this principle cannot be realized. This is possible, however, for nonlinear dynamical semigroups for some random variables called p-collison-type variables in analogy to the Boltzmann 2-collision problem.