Treating random sequential addition via the replica method

TL;DR

This paper explores a novel theoretical approach using the replica method to model non-equilibrium random sequential addition processes by mapping them onto equilibrium systems, enabling predictions of structural properties.

Contribution

It introduces a new application of the replica method to analyze non-equilibrium random sequential addition, bridging the gap between equilibrium theory and non-equilibrium phenomena.

Findings

Theoretical predictions match numerical simulations.

The replica method effectively models non-equilibrium structures.

Provides a new framework for non-equilibrium statistical mechanics.

Abstract

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.