A two-scale approach for sampling local free energy minimisers
Abstract
When a free energy admits several local minimisers, the associated mean-field particle system exhibits a metastable behavior, undergoing random transitions between these minimisers. However, when the number of particles is large, these transitions are rare events and typically occur at a time-scale which is out of reach for simulations. In this work, we introduce a system of particles coupled with a slow macroscopic external variable which approximately follows a Langevin dynamics associated to a coarse-grained free energy. The empirical distribution of the particle system thus samples all local minimisers of the initial free energy, with transition times which are now independent from the number of particles. The construction is inspired by a theoretical tool: the two-scale approach for proving log-Sobolev inequalities for Gibbs measures.
Related
- Exact L2-growth profiles for the free wave equation: Sharp constants, critical regularity, and local energy decay
- Bubble Tree Convergence for Minimisers of a Regularised Baby-Skyrme Model
- Rapid reconstruction-free classification from Lissajous sparse sampling using deep learning
- A sampling Lovász Local Lemma
- A Counting and Sampling Lovász Local Lemma
BibTeX
@misc{leclerc2026twoscale,
title = {{A two-scale approach for sampling local free energy minimisers}},
author = {Antoine Leclerc and Pierre Monmarché},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36195},
eprint = {2609.36195},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36195},
}
RIS
TY - UNPB
TI - A two-scale approach for sampling local free energy minimisers
AU - Antoine Leclerc
AU - Pierre Monmarché
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36195
UR - https://arxiv.org/abs/2609.36195
AB - When a free energy admits several local minimisers, the associated mean-field particle system exhibits a metastable behavior, undergoing random transitions between these minimisers. However, when the number of particles is large, these transitions are rare events and typically occur at a time-scale which is out of reach for simulations. In this work, we introduce a system of particles coupled with a slow macroscopic external variable which approximately follows a Langevin dynamics associated to a coarse-grained free energy. The empirical distribution of the particle system thus samples all local minimisers of the initial free energy, with transition times which are now independent from the number of particles. The construction is inspired by a theoretical tool: the two-scale approach for proving log-Sobolev inequalities for Gibbs measures.
ER -