In the present paper we consider a simple model of stochastic systems, which include basic systems of quantum physics. In the framework of this model we demonstrate the Boltzman entropy, second law of thermodynamics and Gibbs theorem as classical achievements on one side, and several possible entropies of the Shannon theory, and their relations to the Boltzman entropy on the other side. We introduce an information transmission in the systems under consideration, define the Shannon information in a variable about the system state, and formulate the concept of information capacity of a system. We explicitly evaluate the capacity of a system governed by the Bose–Einstein law (a boson channel) and that governed by the Fermi–Dirac law (a fermion channel). ©1999 American Institute of Physics.