Most probable path of an active Brownian particle

Abstract

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager--Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the $\ell$ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

References in corpus (16)

• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Green Algae as Model Organisms for Biological Fluid Dynamics
• Self-Propelled Rods near Surfaces
• Activated escape of a self-propelled particle from a metastable state
• Onsager's variational principle in active soft matter
• Dynamical Clustering Interrupts Motility Induced Phase Separation in Chiral Active Brownian Particles
• Stochastic actions for diffusive dynamics: Reweighting, sampling, and minimization
• Kinetics of motility-induced phase separation and swim pressure
• Escape kinetics of self-propelled particles from a circular cavity
• Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
• Optimal navigation of microswimmers in complex and noisy environments
• The Onsager-Machlup Integral for Non-reciprocal Systems with Odd Elasticity
• Experimental measurement of relative path probabilities and stochastic actions
• Swimmer dynamics in externally-driven fluid flows: The role of noise
• The control of particles in the Stokes limit

Cited by in corpus (6)

• Efficient control protocols for an active Ornstein-Uhlenbeck particle
• The most probable path of Active Ornstein-Uhlenbeck particles
• Stability of interlocked self-propelled dumbbell clusters
• Most probable paths for active Ornstein-Uhlenbeck particles
• Statistical formulation of Onsager-Machlup variational principle
• Irreversibility of stochastic state transitions in Langevin systems with odd elasticity