  We consider energetics of a free quantum Brownian particle coupled to
thermostat of temperature $T$ and study this problem in terms of the lately
formulated quantum analogue of the energy equipartition theorem. We show how
this quantum counterpart can be derived from the Callen-Welton
fluctuation-dissipation relation and rephrased in terms of superstatistics. We
analyse the influence of the system-thermostat coupling strength and the memory
time of the dissipation kernel on statistical characteristics of the particle
energy and its specific heat.
