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While many physical processes are non-equilibrium in nature, the theory andmodeling of such phenomena lag behind theoretical treatments of equilibriumsystems. The diversity of powerful theoretical tools available to describeequilibrium systems has inspired strategies that map non-equilibrium systemsonto equivalent equilibrium analogs so that interrogation with standardstatistical mechanical approaches is possible. In this work, we revisit themapping from the non-equilibrium random sequential addition process onto anequilibrium multi-component mixture via the replica method, allowing fortheoretical predictions of non-equilibrium structural quantities. We validatethe above approach by comparing the theoretical predictions to numericalsimulations of random sequential addition.

Treating random sequential addition via the replica method