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 so
lutions show then the isothermal Maxwell daemon property reported so far fo
r just a few exceptional non-trivial models. Owing to specific dynamical ef
fects in the particle-phonon system, the resulting long-time particle site
occupation probabilities are incompatible with the usual equilibrium statis
tical thermodynamics.