Learning nonequilibrium statistical mechanics and dynamical phase transitions
Abstract Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also poses new challenges as the distribution evolves over...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-02-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-45172-8 |
| _version_ | 1827326899109494784 |
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| author | Ying Tang Jing Liu Jiang Zhang Pan Zhang |
| author_facet | Ying Tang Jing Liu Jiang Zhang Pan Zhang |
| author_sort | Ying Tang |
| collection | DOAJ |
| description | Abstract Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also poses new challenges as the distribution evolves over time. Characterizing dynamical phase transitions as an emergent behavior further requires tracking nonequilibrium systems under a control parameter. While a number of methods have been proposed, such as tensor networks for one-dimensional lattices, we lack a method for arbitrary time beyond the steady state and for higher dimensions. Here, we develop a general computational framework to study the time evolution of nonequilibrium systems in statistical mechanics by leveraging variational autoregressive networks, which offer an efficient computation on the dynamical partition function, a central quantity for discovering the phase transition. We apply the approach to prototype models of nonequilibrium statistical mechanics, including the kinetically constrained models of structural glasses up to three dimensions. The approach uncovers the active-inactive phase transition of spin flips, the dynamical phase diagram, as well as new scaling relations. The result highlights the potential of machine learning dynamical phase transitions in nonequilibrium systems. |
| first_indexed | 2024-03-07T14:53:07Z |
| format | Article |
| id | doaj.art-0194edc2b2d2485ba9b9c1ac9abc8507 |
| institution | Directory Open Access Journal |
| issn | 2041-1723 |
| language | English |
| last_indexed | 2024-03-07T14:53:07Z |
| publishDate | 2024-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj.art-0194edc2b2d2485ba9b9c1ac9abc85072024-03-05T19:34:50ZengNature PortfolioNature Communications2041-17232024-02-011511910.1038/s41467-024-45172-8Learning nonequilibrium statistical mechanics and dynamical phase transitionsYing Tang0Jing Liu1Jiang Zhang2Pan Zhang3Institute of Fundamental and Frontier Sciences, University of Electronic Sciences and Technology of ChinaCAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesSchool of Systems Science, Beijing Normal UniversityCAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesAbstract Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also poses new challenges as the distribution evolves over time. Characterizing dynamical phase transitions as an emergent behavior further requires tracking nonequilibrium systems under a control parameter. While a number of methods have been proposed, such as tensor networks for one-dimensional lattices, we lack a method for arbitrary time beyond the steady state and for higher dimensions. Here, we develop a general computational framework to study the time evolution of nonequilibrium systems in statistical mechanics by leveraging variational autoregressive networks, which offer an efficient computation on the dynamical partition function, a central quantity for discovering the phase transition. We apply the approach to prototype models of nonequilibrium statistical mechanics, including the kinetically constrained models of structural glasses up to three dimensions. The approach uncovers the active-inactive phase transition of spin flips, the dynamical phase diagram, as well as new scaling relations. The result highlights the potential of machine learning dynamical phase transitions in nonequilibrium systems.https://doi.org/10.1038/s41467-024-45172-8 |
| spellingShingle | Ying Tang Jing Liu Jiang Zhang Pan Zhang Learning nonequilibrium statistical mechanics and dynamical phase transitions Nature Communications |
| title | Learning nonequilibrium statistical mechanics and dynamical phase transitions |
| title_full | Learning nonequilibrium statistical mechanics and dynamical phase transitions |
| title_fullStr | Learning nonequilibrium statistical mechanics and dynamical phase transitions |
| title_full_unstemmed | Learning nonequilibrium statistical mechanics and dynamical phase transitions |
| title_short | Learning nonequilibrium statistical mechanics and dynamical phase transitions |
| title_sort | learning nonequilibrium statistical mechanics and dynamical phase transitions |
| url | https://doi.org/10.1038/s41467-024-45172-8 |
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