Rethermalization

Rethermalization is the process by which a non-equilibrium many-body system evolves toward a thermal equilibrium state characterized by a temperature (and, where appropriate, chemical potentials) after being driven away from equilibrium by a disturbance such as a quench, external field, or rapid expansion. In this sense, it is the return to a state described by standard statistical ensembles, with energy redistributed among available degrees of freedom through interactions.

The mechanism of rethermalization hinges on scattering and interaction processes that redistribute energy and momentum while respecting conserved quantities. In kinetic theories, this is described by collision integrals in the Boltzmann equation or its quantum analogs, which drive the distribution toward a Maxwell-Boltzmann, Fermi-Dirac, or Bose-Einstein form. The rate depends on the strength and nature of interactions, phase-space constraints, and, in some systems, the presence of conserved quantities or near-integrability that can slow or modify relaxation.

Rethermalization is distinct from prethermalization, where a system reaches a quasi-stationary, non-thermal state that persists for a long time before eventually relaxing. In strictly integrable systems, true thermalization may be inhibited, requiring weak integrability breaking or coupling to an environment to drive the system toward a conventional thermal state.

Timescales of rethermalization vary widely by system: ultracold atomic gases may rethermalize after ms to s timescales; solids often exhibit electron- or phonon-mediated relaxation on femtosecond to picosecond scales; plasmas and quark–gluon plasmas have their own characteristic rapid relaxation dynamics. Rethermalization remains central to understanding how isolated quantum systems approach equilibrium and how conservation laws and interactions shape that approach.