Machine-learning Iterative Calculation of Entropy for Physical Systems

TL;DR

This paper introduces MICE, a machine learning-based iterative method for accurately estimating the entropy of complex physical systems by leveraging mutual information, applicable to both thermal and athermal systems.

Contribution

The paper presents a novel entropy calculation method using machine learning and mutual information, improving accuracy and generality over existing approaches.

Findings

Accurately estimates entropy of classical spin systems.

Identifies the jamming point in soft disk mixtures.

Provides mutual information as a diagnostic tool.

Abstract

Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current methods for entropy estimation suffer either from a high computational cost, lack of generality or inaccuracy, and inability to treat complex, strongly interacting systems. In this paper, we present a novel method, termed MICE, for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems, and identify the jamming point of a bidisperse mixture of soft disks. Lastly, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.