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

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