  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.
