# A probabilistic framework for irreversible kinetics

Source: [A probabilistic framework for irreversible kinetics](<https://www.sota2.com/research/paper/696dba7fe25ad2fa9d1ecc8e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-08-05T05:00:18.080Z

Authors: Manas V. Upadhyay

Published: 2026-01-14T15:43:53.000Z

## Abstract

A probabilistic framework for irreversible kinetics is proposed in which a constrained path functional $\\mathcal J$ encodes constitutive physics and observations on the admissible history space $\\mathcal H\_{\\rm ad}$, while a discrete Gibbs-type measure proportional to $\\exp(-\\mathcal J/\\Theta)$ assigns probabilities to a candidate set $\\mathcal H\\subseteq\\mathcal H\_{\\rm ad}$. The framework unifies forward-in-time evolution and inverse inference, which differ only through observations and how they constrain admissible histories. The parameter $\\Theta$ controls epistemic uncertainty, and the measure is interpreted as a Bayesian posterior over histories. Maximizing this posterior is equivalent to simultaneous minimization of $\\mathcal J$ over $\\mathcal H$, distinguishing the continuous minimizer $h\_{\\rm cont}$ over $\\mathcal H\_{\\rm ad}$ from the discrete maximum a posteriori (MAP) history $h\_{\\rm MAP}$ over $\\mathcal H$. As $\\Theta\\to0$, the posterior concentrates on the discrete MAP set. For generalized standard material(GSM)-type incremental energy--dissipation functionals, seven forward-in-time examples show that, despite using the same incremental functionals, causal GSM evolution is generally only incrementally optimal. When minimizers are unique, observations are absent, and $h\_{\\rm cont}\\in\\mathcal H$, the strict ordering $\\mathcal J(h\_{\\rm cont})=\\mathcal J(h\_{\\rm MAP})\<\\mathcal J(h\_{\\rm GSM})$ holds, showing that the GSM history does not minimize the cost of the entire history. Finally, an endpoint-conditioned inverse problem with nonconvex energy demonstrates the finite-$\\Theta$ capability of the framework to infer unobserved states and quantify uncertainty over admissible histories.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2601.10763>)

[PDF](<https://arxiv.org/pdf/2601.10763.pdf>)