 0398 David Ruelle
 Extending the definition of entropy to nonequilibrium steady states
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Mar 9, 03

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Abstract. We study the nonequilibrium statistical mechanics of a finite classical
system subjected to nongradient forces $\xi$ and maintained at fixed
kinetic energy (HooverEvans isokinetic thermostat). We assume that
the microscopic dynamics is sufficiently chaotic (GallavottiCohen
chaotic hypothesis) and that there is a natural nonequilibrium steady
state $\rho_\xi$. When $\xi$ is replaced by $\xi+\delta\xi$ one can
compute the change $\delta\rho$ of $\rho_\xi$ (linear response) and
define an entropy change $\delta S$ based on energy considerations.
When $\xi$ is varied around a loop, the total change of $S$ need not
vanish: outside of equilibrium the entropy has curvature. But at
equilibrium (i.e. if $\xi$ is a gradient) we show that the curvature is
zero, and that the entropy $S(\xi+\delta\xi)$ near equilibrium is well
defined to second order in $\delta\xi$.
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