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Mesoscopic non-equilibrium thermodynamics for quantum systems

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  • Bedeaux, D.
  • Mazur, P.

Abstract

An extension of the scheme of non-equilibrium thermodynamics developed previously is given for quantum mechanical systems. A master equation for the density 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 equations. A new element, compared to the classical Langevin equations, is a 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 wellknown problems illustrates the usefullness of this method.

Suggested Citation

  • Bedeaux, D. & Mazur, P., 2001. "Mesoscopic non-equilibrium thermodynamics for quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(1), pages 81-100.
    • Handle: RePEc:eee:phsmap:v:298:y:2001:i:1:p:81-100
    DOI: 10.1016/S0378-4371(01)00223-0
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    Cited by:

    1. Pérez-Madrid, A., 2007. "Nonequilibrium entropy. Characterization of stationary states," Energy, Elsevier, vol. 32(4), pages 301-305.

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