Kinetics of clusters in a binary linear system

We consider the stochastically time-dependent behaviour of a binary linear chain of N units at temperature T and in an external field H. The kinetics is described in terms of clusters (sequences) of specified numbers of units in the same state. A coarse-grained master equation for the cluster densities on the chain is derived by an approximation due to Felderhof. We calculate the relaxation time of fluctuations, and the zero-field frequency-dependent susceptibility, of the fraction of units in a given state. Our results are compared to the phenomenological theory of irreversible thermodynamics.