The Lorentz Gas: A Paradigm for Nonequilibrium Stationary States [chapter]

C. P. Dettmann
2000 Hard Ball Systems and the Lorentz Gas  
Nonequilibrium stationary states form the building blocks of more complicated nonequilibrium systems as they de ne the transport coe cients appearing in the hydrodynamic equations. Recently, many connections have been made between the microscopic dynamical properties of such systems and the macroscopic transport. Although it is often di cult 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,
more » ... 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 coe cients, 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, thermostatted systems and boundary driven systems. All of these and the connections between them can be understood in some detail using the Lorentz gas.
doi:10.1007/978-3-662-04062-1_12 fatcat:fxk533y2grgirpoqrtwatiyrnq