Inhomogeneous random sequential adsorption with equilibrium initial conditions

We study the exact solution for the irreversible addition of nearest-neighbor hard-core particles to a lattice structure occupied at an initial time by particles of the same kind that are in a thermal equilibrium state. The adsorption probabilities are inhomogeneous in both time and space. This problem is attacked via the Bethe lattice, whose topology provides local forms of inverse relations with site coverages as controlling variables, separately for equilibrium as well as for nonequilibrium regimes. It is shown that the interference of the two inverse formats does not break their locality, due to a factorization property of equilibrium multisite correlations. The complete inverse solution is used to point out the absence of nonequilibrium phase transitions within irreversible stochastic dynamics.