An algorithm for series expansions based on hierarchical rate equations

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. PACS numbers: 05.50.+q,05.20.-y,05.70.Ln Most dynamical models in equilibrium and nonequilibrium statistical mechanics can be described by a set of hierarchical rate equations: random sequential adsorptions (RSA) and their variants [1], diffusion-reaction models [2], and kinetic Ising models [3]. The specifications of interactions between the components of the system or interactions between the environment and the system give a deterministic time evolution for the distribution functions once the initial condition of the system is given. Exact solutions are often