Non-equilibrium Thermodynamics for Quantum Systems

Abstract

The extension of the scheme of mesoscopic non-equilibrium thermodynamics developed for quantum mechanical systems by Bedeaum and Mazur (2001) is discussed. This scheme gives a master equation for the density matrix of the system. Onsager relations are given. Application to a spin system gives the Bloch equations. The application to a one-dimensional harmonic oscillator results in equations which make it possible to calculate the Green functions. For the last case we derive, as a new alternative, quantum mechanical Langevin equations. Compared to the classical Langevin equations a new element is random velocity. The correlation of the random velocity with the random force then results from the zero point motion of the oscillator. The application of mesoscopic non-equilibrium thermodynamics to these well known problems illustrates the usefullness of this method.