A Quantum Theory of Thermodynamic Relaxation

Abstract: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck-like equation is derived. The latter was examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. Key words: quantum relaxation, Markov processes, non-equilibrium thermodynamics. Despite the great progress in contemporary quantum statistical physics [1], there are still problems in the applicability of the developed concept to complex systems such as in chemistry. As a rule, the theory of quantum relaxation is much less elaborated than that of the equilibrium. This fact is not surprising since the same situation holds in classical physics. In the latter, the most powerful theory of relaxation phenomena is due to the Markov approximation of processes in Nature. There are some attempts to develop a corresponding quantum idealization [2], e.g. Glauber-Sudarshan [3] and Husimi [4] presentations, but they are less universal. The most general approach to quantum dissipation consists in the projection of the Universe dynamics to those of a system and environment. This mean