Calculating the entropy of physical systems with Machine Learning*

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. We present a novel method, termed MICE (Machine-learning Iterative Calculation of Entropy) 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 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 spheres. 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.