Active processes in one dimension

Abstract

We consider the thermal and athermal overdamped motion of particles in 1D geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent spin constitutes the simplest model of active particles (run-and-tumble processes) where the violation of the equipartition principle and of the Sutherland-Einstein relation can be studied in detail even when there is generalized reversibility. We give an example (with four spin values) where the irreversibility of the translational motion manifests itself only in higher-order (than two) time correlations. We derive a generalized telegraph equation as the Smoluchowski equation for the spatial density for an arbitrary number of spin values. We also investigate the Arrhenius exponential law for run-and-tumble particles, due to their activity the slope of the potential becomes important in contrast to the passive diffusion case and activity enhances the escape from a potential well (if that slope is high enough). Finally, in the absence of a driving velocity, the presence of internal currents such as in the chemistry of molecular motors may be transmitted to the translational motion and the internal activity is crucial for the direction of the emerging spatial current.

26 pages, 3 figures

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Cited by in corpus (56)

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• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
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• Condensation transition in the late-time position of a Run-and-Tumble particle
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Occupation time of a run-and-tumble particle with resetting
• Exact spectral solution of two interacting run-and-tumble particles on a ring lattice
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• Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
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• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
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• Active Brownian Particles in a Circular Disk with an Absorbing Boundary
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• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
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• Dynamics of switching processes: general results and applications to intermittent active motion
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• Tuning attraction and repulsion between active particles through persistence
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• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions
• Non-reciprocal interactions between condensates in chemically active mixtures
• The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation
• Universal framework for the long-time position distribution of free active particles