Mpemba effect on near-complete graphs with independence Metropolis–Hastings dynamics
- 1Max Planck Institute for the Physics of Complex Systems
- 2University of Virginia
- 3UNIVERSITY OF VIRGINIA;
Abstract
We use independence Metropolis–Hastings dynamics on a complete graph as a testbed to investigate the Mpemba effect—a striking anomalous relaxation phenomenon characterized by a nonmonotonic dependence of the relaxation dynamics on the initial condition. Such nonmonotonicity is exemplified whenever a system prepared at a high temperature cools down to an environment’s temperature more efficiently than an identical system initialized at a lower temperature, which is closer to the target. We show that Metropolis dynamics on a complete graph does not exhibit the Mpemba effect, whereas the effect can arise on non-complete graphs with the same dynamics. Alternatively, even on a complete graph with Metropolis dynamics, anomalous relaxation can occur if the initial states are at equilibrium in the presence of a potential that is absent when the system is coupled to the target bath. Finally, we consider the more general case of a system relaxing with independence Metropolis–Hastings dynamics. We show that, with nonuniform priors, the dynamics can exhibit nonanalyticity in the relaxation direction, akin to a dynamical phase transition, and thus the Mpemba effect–even on a complete graph.
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BibTeX
@article{klich2026mpemba,
title = {{Mpemba effect on near-complete graphs with independence Metropolis–Hastings dynamics}},
author = {Israel Klich and Marija Vucelja},
journal = {Journal of Physics A Mathematical and Theoretical},
year = {2026},
month = jun,
doi = {10.1088/1751-8121/ae7228},
url = {https://doi.org/10.1088/1751-8121/ae7228},
note = {CC BY},
}
RIS
TY - JOUR
TI - Mpemba effect on near-complete graphs with independence Metropolis–Hastings dynamics
AU - Israel Klich
AU - Marija Vucelja
PY - 2026
DA - 2026/06/23
JO - Journal of Physics A Mathematical and Theoretical
DO - 10.1088/1751-8121/ae7228
UR - https://doi.org/10.1088/1751-8121/ae7228
AB - We use independence Metropolis–Hastings dynamics on a complete graph as a testbed to investigate the Mpemba effect—a striking anomalous relaxation phenomenon characterized by a nonmonotonic dependence of the relaxation dynamics on the initial condition. Such nonmonotonicity is exemplified whenever a system prepared at a high temperature cools down to an environment’s temperature more efficiently than an identical system initialized at a lower temperature, which is closer to the target. We show that Metropolis dynamics on a complete graph does not exhibit the Mpemba effect, whereas the effect can arise on non-complete graphs with the same dynamics. Alternatively, even on a complete graph with Metropolis dynamics, anomalous relaxation can occur if the initial states are at equilibrium in the presence of a potential that is absent when the system is coupled to the target bath. Finally, we consider the more general case of a system relaxing with independence Metropolis–Hastings dynamics. We show that, with nonuniform priors, the dynamics can exhibit nonanalyticity in the relaxation direction, akin to a dynamical phase transition, and thus the Mpemba effect–even on a complete graph.
SN - 1751-8113
SN - 1751-8121
ER -