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The orientational memory of particles can serve as an effective measure ofdiffusivity, spreading, and search efficiency in complex stochastic processes.We develop a theoretical framework to describe the decay of directionalcorrelations in a generic class of stochastic active processes consisting ofdistinct states of motion characterized by their persistence and switchingprobabilities between the states. For exponentially distributed sojourn times,the orientation autocorrelation is analytically derived and the characteristictimes of its crossovers are obtained in terms of the persistence of each stateand the switching probabilities. We show how non-exponential sojourn-timedistributions of interest, such as Gaussian and power-law distributions, canresult from history-dependent transitions between the states. The relaxationbehavior of the correlation function in such non-Markovian processes isgoverned by the history-dependence of the switching probabilities and cannot besolely determined by the mean sojourn times of the states.

Orientational Memory of Active Particles in Multistate Non-Markovian Processes