Machine Learning H-theorem

TL;DR

This paper explores the microscopic foundations of the Second Law of Thermodynamics by studying the equilibration of hard disks and employing a DeepSets-based model to understand irreversibility.

Contribution

It introduces a machine learning approach using DeepSets to model the irreversibility of the H-functional in a physical system, linking it to the arrow of time.

Findings

Successfully trained a model to capture irreversibility.

Demonstrated the relation between H-theorem and equilibration.

Provided insights into the microscopic basis of thermodynamic irreversibility.

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.