The Effective Temperature in Elasto-Plasticity of Amorphous Solids

TL;DR

This paper introduces a new, measurable definition of the effective temperature in sheared amorphous solids, linking it to structural features and flow properties without relying on equilibrium assumptions.

Contribution

It provides a novel, practical way to define and measure the effective temperature in elasto-plastic amorphous solids based on structural characteristics.

Findings

The new $T_{\rm eff}$ correlates with flow stress and mean energy.

The definition avoids fluctuation-dissipation theorem limitations.

The approach is supported by theoretical and scaling analysis.

Abstract

An effective temperature $T_{\rm eff}$ which differs from the bath temperature is believed to play an essential role in the theory of elasto-plasticity of amorphous solids. The definition of a measurable $T_{\rm eff}$ in the literature on sheared solids suffers however from being connected to a fluctuation-dissipation theorem which is correct only in equilibrium. Here we introduce a natural definition of $T_{\rm eff}$ based on measurable structural features without recourse to any questionable assumption. The value of $T_{\rm eff}$ is connected, using theory and scaling concepts, to the flow stress and the mean energy that characterize the elasto-plastic flow.