  Quantum decoherence is of primary importance for relaxation to an equilibrium
distribution and, accordingly, for equilibrium processes. We demonstrate how
coherence breaking implies evolution to a microcanonical distribution
(``microcanonical postulate'') and, on that ground, consider an adiabatic
process, in which there is no thermostat. We stress its difference from a
zero-polytropic process, i.e., a process with zero heat capacity but involving
a thermostat. We find the distribution for the adiabatic process and show that
(i) in the classical limit this distribution is canonical, (ii) for macroscopic
systems, the mean values of energy for adiabatic and zero-polytropic processes
are the same, but its fluctuations are different, and (iii) in general,
adiabatic and zero-polytropic processes are different, which is particularly
essential for mesoscopic systems; for those latter, an adiabatic process is in
general irreversible.
