Machine Learning H-theorem
This work addresses a foundational issue in statistical physics for physicists, but appears incremental as it applies an existing method (DeepSets) to a new domain.
The researchers tackled the problem of understanding the H-theorem and its relation to the arrow of time by studying the equilibration of hard disks, using a DeepSets-based model to capture the irreversibility of the H-functional, but no concrete results or numbers are provided.
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.