An algorithm for series expansions based on hierarchical rate equations

TL;DR

This paper introduces a computational algorithm for deriving power series expansions in time for dynamical systems governed by hierarchical rate equations, applicable across various statistical mechanics problems.

Contribution

It presents a novel, general method for series expansions in hierarchical rate equations, including new results for dimer adsorption on a lattice.

Findings

New series expansion algorithm for dynamical systems.

Application to random sequential adsorption of dimers.

Demonstrates broad applicability in statistical mechanics.

Abstract

We propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations. The method is generally applicable to problems in both equilibrium and nonequilibrium statistical mechanics such as random sequential adsorption, diffusion-reaction dynamics, and Ising dynamics. New result of random sequential adsorption of dimers on a square lattice is presented.