05-346 G. L. Sewell

Quantum Macrostatistical Theory of Nonequilibrium Steady States (136K, TeX) Sep 30, 05

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Abstract. We provide a general macrostatistical formulation of=20 nonequilibrium steady states of reservoir driven quantum systems.=20 This formulation is centred on the large scale properties of the=20 locally conserved hydrodynamical observables, and our basic physical=20 assumptions comprise (a) a chaoticity hypothesis for the nonconserved=20 currents carried by these observables, (b) an extension of Onsager\rq s=20 regression hypothesis to fluctuations about nonequilibrium states, and=20 (c) a certain mesoscopic local equilibrium hypothesis. On this basis we=20 obtain a picture wherein the fluctuations of the hydrodynamical=20 variables about a nonequilibrium steady state execute a Gaussian Markov=20 process of a generalized Onsager-Machlup type, which is completely=20 determined by the position dependent transport coefficients and the=20 equilibrium entropy function of the system. This picture reveals that=20 the transport coefficients satisfy a generalized form of the Onsager=20 reciprocity relations in the nonequilibrium situation and that the=20 spatial correlations of the hydrodynamical observables are generically=20 of long range. This last result constitutes a model-independent quantum=20 mechanical generalization of that obtained for special classical=20 stochastic systems and marks a striking difference between the steady=20 nonequilibrium and equilibrium states, since it is only at critical=20 points that the latter carry long range correlations.=20

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