  Small quantum systems non-weakly coupled to a bath become in the quantum
regime surrounded by a cloud of photons or phonons, which modifies their
thermodynamic behavior. Exactly solvable examples are the Brownian motion of a
quantum particle in a harmonic confining potential and coupled to a harmonic
quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a
bosonic bath, as occurs in NMR physics. It appears that the Clausius inequality
$\dbarrm Q\le T\d S$ can be violated. For non-adiabatic changes of system
parameters the rate of energy dissipation can be negative, and, out of
equilibrium, cyclic processes are possible which extract work from the bath.
Experimental setups for testing some of the effects are discussed.
