The Lorentz gas: A paradigm for nonequilibrium stationary states

Nonequilibrium stationary states form the building blocks of more complicated nonequi-librium systems as they deene the transport coeecients appearing in the hydrody-namic equations. Recently, many connections have been made between the microscopic dynamical properties of such systems and the macroscopic transport. Although it is often diicult to visualise or understand the dynamics of systems with many particles, it turns out that the Lorentz gas, a system containing only one moving particle , provides a paradigm with which many of these connections can be exhibited and studied. This article surveys the properties of nonequilibrium stationary states, from thermodynamics to the computation of transport coeecients, demonstrating how the Lorentz gas appears as one of the simplest models. A number of current approaches are considered, including linear response formulae applied to equilibrium systems, ther-mostatted systems and boundary driven systems. All of these and the connections between them can be understood in some detail using the Lorentz gas.