Stationary superstatistics distributions of trapped run-and-tumble particles

Abstract

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics, and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

15 pages, 10 figures

References in corpus (38)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• The Mechanics and Statistics of Active Matter
• Motility-Induced Phase Separation
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• How far from equilibrium is active matter?
• Sedimentation of active colloidal suspensions
• Sedimentation, trapping, and rectification of dilute bacteria
• A self-propelled particle in an external potential: is there an effective temperature?
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Emergent vortices in populations of colloidal rollers
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Dynamics of Self-Propelled Particles Under Strong Confinement
• From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
• From time series to superstatistics
• Effective temperature of active matter
• Brownian Particles far from Equilibrium
• Active colloidal suspensions exhibit polar order under gravity
• Effective Temperature of Red Blood Cell Membrane Fluctuations
• Generalized entropies and the transformation group of superstatistics
• Superstatistics, thermodynamics, and fluctuations
• The Effective Temperature Concept Tested in an Active Colloid Mixture
• Activity controls fragility: A Random First Order Transition Theory for an active glass
• Active escape dynamics: the effect of persistence on barrier crossing
• Coarse-grained distributions and superstatistics
• A General Nonlinear Fokker-Planck Equation and its Associated Entropy
• From single-particle to collective effective temperatures in an active fluid of self-propelled particles
• Modeling the dynamics of a tracer particle in an elastic active gel
• Linear response and correlation of a self-propelled particle in the presence of external fields
• Lévy flights and self-similar exploratory behaviour of termite workers: beyond model fitting
• Nanoscale dynamics and the fluctuation-dissipation-relation in an aging polymer glass
• Overdamped limit and inverse friction expansion for the Brownian motion in an inhomogeneous medium
• Generalized Archimedes' principle in active fluids
• Forces in inhomogeneous open active-particle systems
• The q-exponential family in statistical physics
• Probing the Fluctuation-Dissipation Theorem in a Perrin-like Experiment

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• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Long time position distribution of an active Brownian particle in two dimensions
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Run-and-tumble motion: field theory and entropy production
• Non-crossing run-and-tumble particles on a line
• The convex hull of the run-and-tumble particle in a plane
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• Linear response theory and Green-Kubo relations for active matter
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Generalized Ornstein-Uhlenbeck Model for Active Motion
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Occupation time of a run-and-tumble particle with resetting
• Dynamics and escape of active particles in a harmonic trap
• Velocity and diffusion constant of an active particle in a one dimensional force field
• The entropy production of an active particle in a box
• Transport of active particles in an open-wedge channel
• Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions
• Time to reach the maximum for a stationary stochastic process
• Calorimetry for active systems
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Analyzing Spatio-Temporal Dynamics of Dissolved Oxygen for the River Thames using Superstatistical Methods and Machine Learning
• Mittag-Leffler functions in superstatistics
• Encounter-based model of a run-and-tumble particle
• Spatio-temporal complexity of power-grid frequency fluctuations
• Current fluctuations in an interacting active lattice gas
• Generalized disorder averages and current fluctuations in run and tumble particles
• Optimal mean first-passage time of a run-and-tumble particle in a class of one-dimensional confining potentials
• Statistical Field Theory and Effective Action Method for scalar Active Matter
• Active Random Walks in One and Two Dimensions
• Nonequilibrium steady state of trapped active particles
• Run-and-tumble particle in one-dimensional potentials: mean first-passage time and applications
• Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle
• Active noise-driven particles under space-dependent friction in one dimension
• Exact solution of a boundary tumbling particle system in one dimension
• Confined run and tumble particles with non-Markovian tumbling statistics
• Pushing run-and-tumble particles through a rugged channel
• Effective temperatures for single particle system under dichotomous noise
• Effect of initial conditions on current fluctuations in non-interacting active particles
• Run-and-tumble motion in trapping environments
• Survival probability and position distribution of a run and tumble particle in $U(x)=\alpha |x|$ potential with an absorbing boundary
• Polymer Concentration Regimes from Fractional Microrheology
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Local entropy production rate of run-and-tumble particles
• Trapping of a run-and-tumble particle in an inhomogeneous domain: the weak noise limit
• Random diffusivity scenarios behind anomalous non-Gaussian diffusion
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• From Attraction to Repulsion: Emergent Interactions in Harmonically Coupled Active Binary System
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Fluctuations of water quality time series in rivers follow superstatistics
• Run-and-tumble particle with saturating rates
• Mean first passage times of higher-dimensional velocity jump processes