Mpemba effect in many-body systems near equilibrium
Phys. Rev. B 114, 074306 – Published 11 August, 2026
DOI: https://doi.org/10.1103/cthl-v65b
Abstract
The Mpemba effect, in which a system initially farther from equilibrium relaxes faster than a closer one, has been observed in a wide variety of linear and nonlinear systems. Here we develop a unified framework for the Mpemba effect in many-body systems near equilibrium based on the spectral geometry of the relaxation operator. We distinguish a nonuniform Mpemba effect, associated with a crossing of global distances to equilibrium, from a strict componentwise Mpemba effect, in which the initially hotter state remains larger in every degree of freedom yet relaxes faster. We show that reciprocal systems admit only the former, whereas reciprocity breaking renders the relaxation operator non-normal and can enable the latter. These results identify reciprocity and non-normality as key ingredients governing anomalous relaxation in linear many-body systems.
