Correlations and Memory Effects in Active Processes with Distinct Motility States.

The stochastic dynamics of active particles with distinct motility states is studied analytically. A theoretical framework is developed to describe a generic class of stochastic processes consisting of two states characterized by their activity coefficients and velocity distributions. The generalized activity of each state may range from being antipersistent (slower than diffusion) to persistent motion. The mean square displacement and velocity autocorrelations are obtained analytically for exponentially distributed sojourn times in each state. Various timescales for orientational correlations are characterized and the asymptotic diffusion constant is derived. It is shown how extra memory effects introduced by age-dependent switching probabilities between the states enhance the orientational correlations in non-Markovian processes with power-law sojourn time distributions.