Abstract
A standard quantum model of the interacting particle vs. single-mode phonon system under the influence of a thermodynamic bath is considered for very specific values of the parameters involved. The resulting computer-exact solutions show then the isothermal Maxwell daemon property reported so far for just a few exceptional non-trivial models. Owing to specific dynamical effects in the particle-phonon system, the resulting long-time particle site occupation probabilities are incompatible with the usual equilibrium statistical thermodynamics.