A Quantum-statistical Theory of Transport Processes

Abstract

A quantum-statistical method of finding molecular expressions for kinetic coefficients is formulated so as to be applicable to the case where the external disturbance which made a system deviate from equilibrium can not be taken as a definite additive term in the Hamiltonian of the system, such as the heat conduction and the viscous flow. This method provides an extension of the fluctuation-dissipation theorem to such quantum-mechanical systems. A quantum-statistical expression for the entropy of a non-equilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to give a quantum-statistical basis for the thermodynamics of irreversible processes. Two ways of application of our method to each special system are shown; one is concerned with deriving the phenomenological equations of motion, and the other with calculating the entropy production of the system. Thus, quantum-statistical expressions are obtained for the relaxation time of an energy transfer between two sub-systems and that of momentum relaxation phenomena, and for the coefficients of thermo-electricity.