Irreversible Kinetics Emerges from Bayesian Inference over Admissible Histories

TL;DR

The paper proposes a probabilistic framework for irreversible kinetics by treating histories as incrementally admissible paths and weighting them with a Gibbs-type measure derived from an energy–dissipation action and observational constraints. A single parameter $\Theta$ controls epistemic uncertainty, and the zero-uncertainty limit concentrates on MAP histories, recovering classical deterministic evolution; non-convex energies or coupled constraints can yield multiple MAP histories, capturing metastability. Seven forward-in-time examples across mechanics and thermodynamics demonstrate the emergence of deterministic kinetics as $\Theta \to 0$, while an inverse problem shows how past histories can be inferred from endpoint data within the same framework. The approach unifies forward dynamics and inverse inference under a principled variational basis, with potential implications for quantifying variability, guiding data-driven model discovery, and extending to finite-$\Theta$ metastable regimes.

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.