Inaugural Article: Extending the definition of entropy to nonequilibrium steady states

摘要

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. However, 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.