Solution of Classical Stochastic One-Dimensional Many-Body Systems

We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that describes the asymmetric diffusion of hard core particles in the presence of an external source and instantaneous annihilation. Starting from a master equation formulation of the problem, we show that the density and multipoint correlation functions obey a closed set of integro-differential equations which in turn can be solved numerically and/or analytically.