Machine-learning iterative calculation of entropy for physical systems

Amit Nir, Eran Sela, Roy Beck, Yohai Bar-Sinai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 from a high computational cost, lack of generality, or inaccuracy and inability to treat complex, strongly interacting systems. In this paper, we present a method, termed machine-learning iterative calculation of entropy (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. Finally, 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.

Original languageEnglish
Pages (from-to)30234-30240
Number of pages7
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number48
StatePublished - 1 Dec 2020


  • Entropy estimation | mutual information | machine learning | jamming


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