Orientational memory of active particles in multistate non-Markovian processes

Area of Science:

• Statistical Physics
• Complex Systems
• Stochastic Processes

Background:

• Particle orientational memory is crucial for understanding diffusivity, spreading, and search efficiency in complex stochastic processes.
• Existing models often assume simple state transitions, limiting their applicability to more intricate systems.

Purpose of the Study:

• To develop a theoretical framework for describing the decay of directional correlations in stochastic active processes.
• To analyze the influence of state persistence and switching probabilities on orientational memory.
• To investigate the impact of non-Markovian dynamics on correlation relaxation.

Main Methods:

• Analytical derivation of orientation autocorrelation for exponentially distributed sojourn times.
• Characterization of crossover times based on state persistence and switching probabilities.
• Modeling of nonexponential sojourn-time distributions (Gaussian, power-law) arising from history-dependent transitions.

Main Results:

• The orientation autocorrelation function and its characteristic crossover times were analytically derived.
• Demonstrated that nonexponential sojourn-time distributions arise from history-dependent transitions.
• Established that correlation relaxation in non-Markovian processes depends on history-dependent switching, not just mean sojourn times.

Conclusions:

• The developed theoretical framework accurately describes orientational memory decay in complex stochastic processes.
• History-dependent transitions introduce non-Markovian behavior, significantly altering correlation relaxation dynamics.
• Understanding these dynamics is key for predicting particle search efficiency and spreading in complex environments.