nonrelaxation

Nonrelaxation is a term used to describe a situation in which a system does not return to a conventional equilibrium state after a disturbance, or does so only on timescales that are effectively infinite for the observation at hand. It can refer to the persistence of non-equilibrium states, non-decaying correlations, or a steady state that remains out of thermodynamic equilibrium despite the absence of continuous driving. The concept encompasses both true non-relaxation, where relaxation to equilibrium is never reached in practice, and extremely slow relaxation that appears effectively permanent within experimental or observational windows.

In condensed matter and materials science, nonrelaxation often appears in glassy and disordered systems. Glasses and spin glasses exhibit extremely slow dynamics, aging, and memory effects, with correlation functions decaying so slowly that the system fails to reach equilibrium on practical timescales. Non-relaxation can also arise in driven or constrained systems where frustration or kinetic constraints prevent relaxation to a simple equilibrium state.

In quantum physics, nonrelaxation is encountered in systems that fail to thermalize. Integrable models, and more recently many-body localized systems, can preserve local information and fail to reach conventional thermal equilibrium, leading to persistent non-thermal steady states or sustained oscillations in observables.

In driven-dissipative contexts, non-equilibrium steady states can exist where continuous input and loss balance but no relaxation to equilibrium occurs. Mechanisms underlying nonrelaxation include disorder, extensive conserved quantities, strong interactions, and external driving forces.

See also: relaxation, non-equilibrium dynamics, aging, glass transition, many-body localization, ergodicity breaking.