Machine Learning H-theorem
Statistical Mechanics
2026-01-07 v3 Machine Learning
Abstract
H-theorem provides a microscopic foundation of the Second Law of Thermodynamics and is therefore essential to establishing statistical physics, but at the same time, H-theorem has been subject to controversy that in part persists till this day. To better understand H-theorem and its relation to the arrow of time, we study the equilibration of randomly oriented and positioned hard disks with periodic boundary conditions. Using a model based on the DeepSets architecture, which imposes permutation invariance of the particle labels, we train a model to capture the irreversibility of the H-functional.
Keywords
Cite
@article{arxiv.2508.14003,
title = {Machine Learning H-theorem},
author = {Ruben Lier},
journal= {arXiv preprint arXiv:2508.14003},
year = {2026}
}