Irreversible Kinetics Emerges from Bayesian Inference over Admissible Histories

TL;DR

This paper introduces a Bayesian probabilistic framework for irreversible kinetics, linking classical deterministic evolution with stochastic inference over histories, demonstrated through multiple examples and inverse problems.

Contribution

It presents a novel Bayesian formulation of irreversible kinetics that incorporates uncertainty and allows for multiple histories in non-convex settings.

Findings

Classical deterministic evolution emerges as a zero-uncertainty limit.

Multiple competing histories are possible in non-convex energy landscapes.

The framework successfully infers unknown histories from sparse observations.

Abstract

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.