Identifying nonequilibrium degrees of freedom in high-dimensional stochastic systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911105766391808 |
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| author | Ji, Catherine Raj, Ravin Eysenbach, Benjamin Reddy, Gautam |
| author_facet | Ji, Catherine Raj, Ravin Eysenbach, Benjamin Reddy, Gautam |
| contents | Any coarse-grained description of a nonequilibrium system should faithfully represent its latent irreversible degrees of freedom. However, standard dimensionality reduction methods typically prioritize accurate reconstruction over physical relevance. Here, we introduce a model-free approach to identify irreversible degrees of freedom in stochastic systems that are in a nonequilibrium steady state. Our method leverages the insight that a black-box classifier, trained to differentiate between forward and time-reversed trajectories, implicitly estimates the local entropy production rate. By parameterizing this classifier as a quadratic form of learned state representations, we obtain nonlinear embeddings of high-dimensional state-space dynamics, which we term Latent Embeddings of Nonequilibrium Systems (LENS). LENS effectively identifies low-dimensional irreversible flows and provides a scalable, learning-based strategy for estimating entropy production rates directly from high-dimensional time series data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying nonequilibrium degrees of freedom in high-dimensional stochastic systems Ji, Catherine Raj, Ravin Eysenbach, Benjamin Reddy, Gautam Statistical Mechanics Biological Physics Any coarse-grained description of a nonequilibrium system should faithfully represent its latent irreversible degrees of freedom. However, standard dimensionality reduction methods typically prioritize accurate reconstruction over physical relevance. Here, we introduce a model-free approach to identify irreversible degrees of freedom in stochastic systems that are in a nonequilibrium steady state. Our method leverages the insight that a black-box classifier, trained to differentiate between forward and time-reversed trajectories, implicitly estimates the local entropy production rate. By parameterizing this classifier as a quadratic form of learned state representations, we obtain nonlinear embeddings of high-dimensional state-space dynamics, which we term Latent Embeddings of Nonequilibrium Systems (LENS). LENS effectively identifies low-dimensional irreversible flows and provides a scalable, learning-based strategy for estimating entropy production rates directly from high-dimensional time series data. |
| title | Identifying nonequilibrium degrees of freedom in high-dimensional stochastic systems |
| topic | Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2508.08247 |