Thermodynamics and phase coexistence in nonequilibrium steady states
I review recent work focussing on whether thermodynamics can be extended to nonequilibrium steady states (NESS). A central issue is the possibility of consistent definitions of temperature T and chemical potential mu for systems in NESS. The testing-grounds are simple, far-from-equilibrium lattice models with stochastic dynamics. Each model includes a drive that maintains the system far from equilibrium, provoking particle and/or energy flows; for zero drive the system approaches equilibrium. Analysis and numerical simulation show that for spatially uniform NESS, coexistence with an appropriate reservoir yields consistent definitions of T and mu are possible, provided a particular kind of rate (that proposed by Sasa and Tasaki ) is used for exchanges of particles and energy between systems . Consistent definitions are not possible for nonuniform NESS . The functions T and mu for isolated phases cannot be used to predict the properties of coexisting phases in a single, phase-separated system . Investigation of simple far-from-equilibrium systems exhibiting phase separation leads to the conclusion that phase coexistence is not well defined in this context. This is because the properties of the coexisting nonequilibrium systems depend on how they are placed in contact, as verified in the driven lattice gas with attractive interactions, and in the two-temperature lattice gas, under (a) weak global exchange between uniform systems, and (b) phase-separated (nonuniform) systems. Thus, far from equilibrium, the notions of universality of phase coexistence (i.e., independent of how systems exchange particles and/or energy), and of phases with intrinsic properties (independent of their environment) are lost.
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