Mpemba effect in many-body systems near equilibrium
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 non-uniform 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.
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BibTeX
@article{benabdallah2026mpemba,
title = {{Mpemba effect in many-body systems near equilibrium}},
author = {P. Ben-Abdallah},
journal = {Physical Review B},
year = {2026},
month = aug,
doi = {10.1103/cthl-v65b},
url = {https://hal.science/hal-05760327v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Mpemba effect in many-body systems near equilibrium
AU - P. Ben-Abdallah
PY - 2026
DA - 2026/08/11
JO - Physical Review B
DO - 10.1103/cthl-v65b
UR - https://hal.science/hal-05760327v1
AB - 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 non-uniform 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.
SN - 2469-9950
SN - 2469-9969
ER -