Thermodynamics and Small Quantum Systems

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 ¯ dQ ≤ T dS 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. 1 Introduction The microscopic basis of thermodynamics is statistical physics and equilibrium is described by the Gibbs distribution. It is typically taken for granted that, when going to the quantum regime, the classical Gibbs distribution can just be replaced by its quantum analog. It is not often stressed that this is only allowed in case of weak coupling with the bath. When that coupling is not weak, the Gibbs state of the total system (subsystem+bath) leads, after tracing out the bath, to a non-Gibbsian state for the subsystem. This endangers (near-) equilibrium thermodynamics. We analyze the situation for two exactly solvable problems.