Fluctuation-Dissipation Ratio for Compacting Granular Media

TL;DR

This paper explores the concept of an effective temperature in granular media during compaction, using fluctuation-dissipation relations in lattice models, and finds agreement with Edwards' measure under certain conditions.

Contribution

It demonstrates that the fluctuation-dissipation ratio aligns with Edwards' measure in idealized and homogeneous granular compaction models, providing a potential dynamical definition of effective temperature.

Findings

FD ratio matches Edwards' measure at various densities.

Homogeneous compaction yields consistent FD ratios with gravity effects.

Proposes experimental tests for Edwards' measure validity.

Abstract

In this paper we investigate the possibility of a dynamical definition of an effective temperature for compacting granular media in the framework of the Fluctuation-Dissipation (FD) relations. We have studied two paradigmatic models for the compaction of granular media, which consider particles diffusing on a lattice, with either geometrical (Tetris model) or dynamical (Kob-Andersen model) constraints. Idealized compaction without gravity has been implemented for the Tetris model, and compaction with a preferential direction imposed by gravity has been studied for both models. In the ideal case of an homogeneous compaction, the obtained FD ratio is clearly shown to be in agreement with the prediction of Edwards' measure at various densities. Similar results are obtained with gravity only when the homogeneity of the bulk is imposed. In this case the FD ratio obtained dynamically for horizontal displacements and mobility and from Edwards' measure coincide. Finally, we propose experimental tests for the validity of the Edwards' construction through the comparison of various types of dynamical measurements.