aiqbench takeMachine Learning

This research applies DeepSets-based neural networks to infer the thermodynamic arrow of time directly from microscopic dynamics in a hard-disk system. By training models solely on temporal ordering constraints, the study bridges statistical mechanics and machine learning to evaluate how physical relaxation processes naturally align with the Boltzmann H-functional structure. The work advances fundamental understanding at the intersection of quantum/statistical physics principles and AI model architecture.

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Machine Learning the H-theorem

arXivJuly 29, 20262 min read

arXiv:2508.14003v4 Announce Type: replace-cross Abstract: The H-theorem provides a microscopic foundation for the Second Law of Thermodynamics and therefore occupies a central place in statistical physics. At the same time, its relation to microscopic reversibility has remained conceptually subtle. To investigate how an arrow of time may be inferred directly from microscopic data, we study the relaxation of randomly initialized hard disks in a periodic box. We construct a permutation-invariant neural network based on the DeepSets architecture. The model is trained only to assign later states a larger scalar value than earlier states. We compare the learned scalar with the Boltzmann H-functional and assess to what extent the dynamics alone lead the model toward the structure implied by the H-theorem.

Abstract:The H-theorem provides a microscopic foundation for the Second Law of Thermodynamics and therefore occupies a central place in statistical physics. At the same time, its relation to microscopic reversibility has remained conceptually subtle. To investigate how an arrow of time may be inferred directly from microscopic data, we study the relaxation of randomly initialized hard disks in a periodic box. We construct a permutation-invariant neural network based on the DeepSets architecture. The model is trained only to assign later states a larger scalar value than earlier states. We compare the learned scalar with the Boltzmann H-functional and assess to what extent the dynamics alone lead the model toward the structure implied by the H-theorem.

Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)

arXiv:2508.14003 [cond-mat.stat-mech]

(or arXiv:2508.14003v4 [cond-mat.stat-mech] for this version)

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