Residence time densities for non-Markovian systems. (II). The N-state system

In the preceding paper (Boguñá et al., Physica A 282 (2000) 475), we developed formalism to calculate a probability density for the cumulative time spent in one out of a two-state non-Markovian system of the form S1⇄S2 when the system is observed continuously for a time T. The asymptotic form for the probability density was shown to be Gaussian. In this paper we indicate how to reduce any reacting nearest-neighbor system, i.e., S1⇄S2⇄⋯⇄SN to an equivalent two-state system. This also shows that the probability density for the cumulative residence time in a single state is asymptotic to a Gaussian.