Non-equilibrium statistical mechanics of non-equilibrium damage phenomena

TL;DR

This paper explores applying non-equilibrium statistical mechanics to damage phenomena, developing a formalism that describes fluctuations, energy balance, and effective temperatures in fiber-bundle models with thermal noise and decay.

Contribution

It introduces a novel analogy of Gibbs formalism for non-equilibrium states and develops a path-based approach with effective temperature parameters.

Findings

Fluctuations are described by Gaussian distributions.

An equation of state for non-equilibrium damage is derived.

A formalism for free energy potential in damage phenomena is established.

Abstract

In this paper we investigate the applicability of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with thermal noise and a fiber-bundle model with decay of fibers are considered. Initially we develop an analogy of the Gibbs formalism for nonequilibrium states. Later we switch from the approach of non-equilibrium states to the approach of non-equilibrium paths. Fluctuating behavior in the system is described in terms of effective temperature parameters. An equation of state and an analog of an energy-balance equation are obtained. Also the formalism of the free energy potential is developed. For fluctuations of paths in the system the statistical distribution is found to be Gaussian.