Effective temperature

Effective temperature is a temperature-like parameter used to characterize a system that is not in full thermal equilibrium. Its meaning depends on how it is defined or measured in that system.

Fluctuation–dissipation theorem: A relation connecting spontaneous fluctuations in a system to its response to external perturbations at thermal equilibrium. Its violation in nonequilibrium systems can define an effective temperature by comparing response with fluctuations.
Temperature: A physical quantity that characterizes hotness and determines the direction of heat transfer at equilibrium. Effective temperature borrows its language from this equilibrium state variable.
Glassy dynamics: Slow, history-dependent relaxation found in glasses and other disordered systems. Aging glassy systems can assign a distinct effective temperature to slowly relaxing modes.
Thermodynamic temperature: An equilibrium state variable that sets the direction of spontaneous heat transfer and relates to entropy and energy. Unlike effective temperature, it has a consistent thermodynamic definition at equilibrium.
Linear response theory: A framework for calculating how a system responds to a small external disturbance. Effective temperature can be inferred by relating measured response to spontaneous fluctuations.
Boltzmann distribution: The equilibrium probability distribution assigning states weights proportional to the exponential of negative energy over thermal energy. A nonequilibrium distribution may resemble this form with a fitted effective temperature.
Active matter: Systems of self-driven units that consume energy to produce motion or forces. Effective temperature can summarize enhanced fluctuations, though active forces need not act like heat.
Local thermodynamic equilibrium: An approximation in which small regions of a nonequilibrium system are treated as being in local equilibrium. It assigns local temperatures under conditions that differ from broader effective-temperature constructions.
Einstein relation: A relation between a particle’s diffusion coefficient and mobility in a thermal environment. In driven systems, departures from this relation can be expressed as an effective temperature.
Entropy: A state function that quantifies the number of microscopic arrangements compatible with a macroscopic state. Some definitions connect effective temperature to entropy changes, especially in aging systems.

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