 95168 Eyink, G. L., Lebowitz, J. L., Spohn, H.
 Hydrodynamics and Fluctuations Outside of Local Equilibrium:
Driven Diffusive Systems
(224K, LaTex)
Mar 28, 95

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We derive hydrodynamic equations for systems not in local thermodynamic
equilibrium, that is, where the local stationary measures are ``nonGibbsian'' and do not
satisfy detailed balance with respect to the microscopic dynamics. As a main
example we consider the {\em driven diffusive systems}(DDS), such as electrical
conductors in an applied field with diffusion of charge carriers.
In such systems, the hydrodynamical description is provided by a nonlinear
driftdiffusion equation, which we derive by a microscopic method of {\em
nonequilibrium distributions}. The formal derivation yields a GreenKubo formula for
the bulk diffusion matrix and microscopic prescriptions for the drift velocity
and ``nonequilibrium entropy'' as functions of charge density. Properties of
the hydrodynamical equations are established, including an ``Htheorem'' on
increase of the thermodynamic potential, or ``entropy,'' describing approach
to the homogeneous steadystate. The results are shown to be consistent with
the derivation of the linearized hydrodynamics for DDS by the KadanoffMartin
correlationfunction method and with rigorous results for particular models.
We discuss also the internal noise in such systems, which we show to be
governed by a generalized {\em fluctuationdissipation relation}(FDR), whose
validity is not restricted to thermal equilibrium or to timereversible
systems. In the case of DDS, the FDR yields a version of a relation proposed
some time ago by Price between the covariance matrix of electrical current
noise and the bulk diffusion matrix of charge density. Our derivation of the
hydrodynamical laws is in a formthe socalled ``Onsager forceflux form''
which allows us to exploit the FDR to construct the Langevin description of
the fluctuations. In particular, we show that the probability of large
fluctuations in the hydrodynamical histories is governed by a version of
the Onsager ``principle of least dissipation,'' which estimates the
probability of fluctuations in terms of the Ohmic dissipation required to
produce them and provides a variational characterization of the most probable
behavior as that associated to least (excess) dissipation.
Finally, we consider the relation of longrange spatial correlations in the
steadystate of the DDS and the validity of ordinary hydrodynamical laws. We
discuss also briefly the application of the general methods of this paper to
other cases, such as reactiondiffusion systems or magnetohydrodynamics of plasmas.
 Files:
95168.src(
desc ,
95168.tex )