A system of particles with discrete set of states and constraints on the occupation numbers is studied. The classical Bernoulli scheme of trials and the quantum scheme corresponding to an arbitrary parastatistics are simultaneously considered. The number of particles is not fixed and has a Poisson distribution. It has been proved that, in both cases, the occupation numbers are independent random variables. In the case of the Markovian evolution of probabilities of states of separate particles, a nonlinear equation for the mean occupation numbers has been derived.
Department of Quantum Statistics and Field Theory, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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