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The Brownian motion of a harmonically bound quantum particle and coupled to aharmonic quantum bath is exactly solvable. At low enough temperatures thestationary state is non-Gibbsian due to an entanglement with the bath. Thishappens when a cloud of bath modes around the particle is formed. Equilibriumthermodynamics for particle plus bath together, does not imply standardthermodynamics for the particle itself at low T. Various formulations of thesecond law are then invalid. First, the Clausius inequality can be violated.Second, when the width of the confining potential is suddenly changed, thereoccurs a relaxation to equilibrium during which the rate of entropy productionis partly negative. Third, for non-adiabatic changes of system parameters therate of energy dissipation can be negative, and, out of equilibrium, cyclicprocesses are possible which extract work from the bath. Conditions are putforward under which perpetuum mobile of the second kind, having several workextraction cycles, enter the realm of condensed matter physics.Comment: 6 pages Latex, uses aip-proceedings style files. Proceedings `Quantum  Limits to the Second Law', San Diego, July 200

Quantum Brownian motion and its conflict with the second law