Extending the definition of entropy to nonequilibrium steady states
Ruelle, David
Original · EN
We study the nonequilibrium statistical mechanics of a finite classical system subjected to nongradient forces ξ and maintained at fixed kinetic energy (Hoover-Evans isokinetic thermostat). We assume that the microscopic dynamics is sufficiently chaotic (Gallavotti-Cohen chaotic hypothesis) and that there is a natural nonequilibrium steady state ρξ. When ξ is replaced by ξ+δξ one can compute the change δρ of ρξ (linear response) and define an entropy change δS based on energy considerations. When ξ 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 ξ is a gradient) we show that the curvature is zero, and that the entropy S(ξ+δξ) near equilibrium is well defined to second order in δξ.
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