Nonequilibrium Systems

Abstract

Nonequilibrium system and behavior are briefly reviewed, with an emphasis on recent progress using minimal microscopic models and on implications for macroscopic descriptions…. Our daily life continually confronts us with large systems whose internal processes or external influences are such that standard physical equilibrium descriptions of macroscopic behavior do not apply. Among complex examples are weather, crowds, traffic, financial markets, and so on, and at the other end of the spectrum are simple queuing, processing, and decision-making setups. The most common, most interesting and most complex examples in nature are predominately collective stochastic systems, in which many constituents influence/ interact with each other in some way, and the processes are probabilistic and dissipative. This is true of most examples given above, certainly of the first ones. None of these achieves ordinary equilibrium states of the sort met in thermodynamics; such systems are generically called nonequilibrium systems (NES). In the case of weather, a reason for not going into standard equilibrium is the sun's continual heating of the earth's land surface, oceans, and atmosphere. A feeding mechanism like that also occurs in traffic systems through the entry and exit of vehicles. In addition, traffic transition rates are not set by thermodynamic balances. Traffic can achieve steady states of flow or jammed states. In common with most other nonequilibrium (NE) steady states, these are quite unlike the equilibrium states provided by the standard "general" macroscopic and microscopic descriptions of thermodynamics and statistical mechanics (see Boltzmann and Gibbs). Nevertheless, NES show many similarities to collective equilibrium systems (ES), largely in behavior at a quantitative level. For example, NES and ES classes both include systems showing phase transitions (e.g., in the NE steady state, or in the thermal equilibrium state, respectively), whose phenomenology can typically be qualitatively interpreted in similar terms (using concepts of order parameter, scale invariance, and power laws, etc.).