Nonequilibrium

Nonequilibrium refers to states of physical systems that are not in thermodynamic equilibrium. In such states, macroscopic properties may change with time, and the probability distribution over microscopic configurations is not stationary. By contrast, equilibrium systems have no net flows of energy or matter, obey detailed balance, and can be described by a small set of intensive variables such as temperature, pressure, and chemical potentials.

Nonequilibrium situations arise when a system experiences external driving, exchanges with reservoirs, or internal production of entropy. They feature energy or matter fluxes, such as heat currents, particle diffusion, chemical reactions, or electrical currents. Transient nonequilibrium describes relaxation toward equilibrium after perturbation, while nonequilibrium steady states maintain constant macroscopic properties despite ongoing fluxes.

Fluctuations and dissipation are central to nonequilibrium behavior; entropy production is nonnegative and typically positive except at equilibrium. Theoretical frameworks include nonequilibrium thermodynamics, extended linear response theory near equilibrium, and stochastic thermodynamics for small or fluctuating systems. Mathematical tools commonly used are master equations, Fokker-Planck equations, Boltzmann transport descriptions, and Langevin dynamics.

Applications span chemical reactors, semiconductor devices, biological systems (such as metabolism and signaling networks), climate and ecological dynamics, and driven soft matter. The term covers a wide range of phenomena from rapid electronic transport to slow diffusion, pattern formation, and self-organization driven by continuous fluxes.