Predicting the unobserved: a statistical mechanics framework for non-equilibrium material response with quantified uncertainty

TL;DR

This paper introduces a statistical mechanics framework that infers non-equilibrium material responses from equilibrium data using stochastic trajectory analysis, enabling predictions without direct simulations or experiments.

Contribution

It develops a method to predict far-from-equilibrium behavior from equilibrium data with quantified uncertainty, based on exact relations in stochastic differential equations.

Findings

Inference accuracy decreases as the difference between S and S~ increases.

The approach is demonstrated on polymer-like and glassy systems.

Predictions can be made without direct simulations of the target system.

Abstract

Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible in principle for systems governed by stochastic differential equations, thanks to a set of exact relations between probability densities for trajectories derived from the path integral formalism [1, 2, 3]. In this article, we systematically investigate inferences (in the form of ensemble-averages) drawn on system/process S based on stochastic trajectory data of system/process S~, with quantified uncertainty, to directly address the aforementioned questions. Interestingly, such inferences and their associated uncertainty do not require any simulations or experiments of S. The results are exemplified over two illustrative examples by means of numerical simulations: a one-dimensional system as a prototype for polymers and biological macromolecules, and a two-dimensional glassy system. In principle, the approach can be pushed to the extreme case where S~ is simply comprised of Brownian trajectories, i.e., equilibrium non-interacting particles, and S is a complex interacting system driven far from equilibrium. In practice, however, the "further" S~ is from S, the greater the uncertainty in the predictions, for a fixed number of realizations of system S~.