Statistical mechanics away from equilibrium is in a formative stage, where general concepts slowly emerge. We restrict ourselves here to the study of transport phenomena, especially heat transport, and consider several well-studied classes of systems: finite systems with isokinetic thermostats, infinite classical Hamiltonian systems, infinite quantum spin systems. For those classes we discuss how various physical quantities can be defined. Our review however leaves several basic questions quite open.

What physical quantities make sense in nonequilibrium statistical mechanics?

David Ruelle

Abstract