Generalized Edwards thermodynamics and marginal stability in a driven system with dry and viscous friction

TL;DR

This paper investigates a spring-block model with dry and viscous friction under periodic driving, revealing limitations of Edwards thermodynamics and proposing a generalized framework based on marginally stable states to describe correlation length scaling.

Contribution

It introduces a generalized Edwards thermodynamics framework that accounts for marginal stability and explains correlation length behavior in driven viscous systems.

Findings

Strong driving leads to non-Edwards scaling of correlation length.

A crossover from Edwards to high-energy scaling depends on viscous friction.

The proposed framework successfully describes the correlation length in highly viscous regimes.

Abstract

We consider a spring-block model with both dry and viscous frictions, subjected to a periodic driving allowing mechanically stable configurations to be sampled. We show that under strong driving, the scaling of the correlation length with the energy density is incompatible with the prediction of Edwards statistical approach, which assumes a uniform sampling of mechanically stable configurations. A crossover between the Edwards scaling and the non-standard high energy scaling is observed at energy scales that depend on the viscous friction coefficient. Generalizing Edwards thermodynamics, we propose a statistical framework, based on a sampling of marginally stable states, that is able to describe the scaling of the correlation length in the highly viscous regime.