 05346 G. L. Sewell
 Quantum Macrostatistical Theory of Nonequilibrium Steady States
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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 OnsagerMachlup 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 modelindependent 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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