Edwards thermodynamics for a driven athermal system with dry friction

TL;DR

This paper develops an Edwards thermodynamics framework for a one-dimensional driven athermal system with dry friction, capturing critical behavior and divergence of correlation length through semi-analytical methods.

Contribution

It introduces a semi-analytical transfer operator approach to model dry friction systems and analytically characterizes the divergence of correlation length near a critical point.

Findings

Reproduces the linear divergence of correlation length with energy density.

Identifies an infinite temperature critical point associated with system behavior.

Provides an analytical Gaussian approximation for mechanically stable configurations.

Abstract

We obtain, using semi-analytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear divergence of the correlation length as a function of energy density observed in direct numerical simulations of the model under tapping dynamics. We further characterize analytically this divergence using a Gaussian approximation for the distribution of mechanically stable configurations, and show that it is related to the existence of a peculiar infinite temperature critical point.