Memory and Kovacs effects in the parking-lot model: an approximate statistical-mechanical treatment

TL;DR

This paper develops an approximate statistical-mechanical framework for the parking-lot model, capturing history-dependent phenomena like memory and Kovacs effects in granular compaction.

Contribution

It introduces a 2-parameter generalization of Edwards' formalism to derive kinetic equations that describe memory effects in the parking-lot model.

Findings

The model reproduces memory effects observed in granular compaction.

Approximate kinetic equations successfully describe Kovacs effects.

The approach extends Edwards' formalism to include history-dependent phenomena.

Abstract

The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter generalization of the statistical-mechanical formalism first proposed by Edwards and coworkers. We show that history-dependent effects, such as memory and Kovacs effects, are captured by this approach.