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[References: 19 tit.]

Employing quadratic fermionic and bosonic Hamiltonians for collective and internal subsystems with a linear rotating-wave-approximation coupling, we studied the role of heat-bath statistics on the dynamics of the collective motion. The master equations for the collective occupation number derived directly from the quadratic Hamiltonians and within the Non-Markovian Langevin approach are discussed and their solutions are obtained. Because of the different nature of the heat-bath statistics, the path to equilibrium or the relaxation time is affected as shown in the numerical calculations.