Irreversible Kinetics Emerges from Bayesian Inference over Admissible Histories
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914258084691968 |
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| author | Upadhyay, Manas V. |
| author_facet | Upadhyay, Manas V. |
| contents | A probabilistic formulation of irreversible kinetics is introduced in which incrementally admissible histories are weighted by a Gibbs-type measure built from an energy-dissipation action and observation constraints, with Theta controlling epistemic uncertainty. This measure can be interpreted as a Bayesian posterior over histories. In the zero-uncertainty limit, it concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution by incremental minimization in the convex generalized-standard-material setting, while allowing multiple competing MAP histories for non-convex energies or temporally coupled constraints. This emergence is demonstrated across seven distinct forward-in-time examples and an inverse inference problem of unknown histories from sparse observations via a global constrained minimum-action principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Irreversible Kinetics Emerges from Bayesian Inference over Admissible Histories Upadhyay, Manas V. Statistical Mechanics Machine Learning 74A20, 74D10 A probabilistic formulation of irreversible kinetics is introduced in which incrementally admissible histories are weighted by a Gibbs-type measure built from an energy-dissipation action and observation constraints, with Theta controlling epistemic uncertainty. This measure can be interpreted as a Bayesian posterior over histories. In the zero-uncertainty limit, it concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution by incremental minimization in the convex generalized-standard-material setting, while allowing multiple competing MAP histories for non-convex energies or temporally coupled constraints. This emergence is demonstrated across seven distinct forward-in-time examples and an inverse inference problem of unknown histories from sparse observations via a global constrained minimum-action principle. |
| title | Irreversible Kinetics Emerges from Bayesian Inference over Admissible Histories |
| topic | Statistical Mechanics Machine Learning 74A20, 74D10 |
| url | https://arxiv.org/abs/2601.10763 |