Mesoscopic non-equilibrium thermodynamics for quantum systems

An extension of the scheme of non-equilibrium thermodynamics developed prev iously is given for quantum mechanical systems. A master equation for the d ensity matrix of the system follows from this scheme. Onsager relations are given and derived. Application to a spin system gives the Bloch equations. The application to a one-dimensional damped harmonic oscillator results in equations, which enable us to calculate the usual Green functions. For the last case we derive, as a new alternative, quantum mechanical Langevin equ ations. A new element, compared to the classical Langevin equations, is a r andom velocity. The correlation of the random velocity with the random forc e then results from the zero point motion of the oscillator. The applicatio n of mesoscopic non-equilibrium thermodynamics to these wellknown problems illustrates the usefullness of this method. (C) 2001 Elsevier Science B.V. All rights reserved.