  For a free particle, the coupling to its environment can be the relevant
mechanism to induce quantum behavior as the temperature is lowered. We study
general linear environments with a spectral density proportional to {\omega}^s
at low frequencies and consider in particular the specific heat of the free
damped particle. For super-Ohmic baths with s>=2, a reentrant classical
behavior is found. As the temperature is lowered, the specific heat decreases
from the classical value of k_B/2, thereby indicating the appearence of quantum
effects. However, the classical value of the specific heat is restored as the
temperature approaches zero. This surprising behavior is due to the suppressed
density of bath degrees of freedom at low frequencies. For s<2, the specific
heat at zero temperature increases linearly with s from -k_B/2 to k_B/2. An
Ohmic bath, s=1, is thus very special in the sense that it represents the only
case where the specific heat vanishes at zero temperature.
