A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle

Abstract

We study the probability distribution $P(X_N=X,N)$ of the total displacement $X_N$ of an $N$-step run and tumble particle on a line, in presence of a constant nonzero drive $E$. While the central limit theorem predicts a standard Gaussian form for $P(X,N)$ near its peak, we show that for large positive and negative $X$, the distribution exhibits anomalous large deviation forms. For large positive $X$, the associated rate function is nonanalytic at a critical value of the scaled distance from the peak where its first derivative is discontinuous. This signals a first-order dynamical phase transition from a homogeneous `fluid' phase to a `condensed' phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.

35 pages, 5 figures. An algebraic error in Appendix B of the previous version of the manuscript has been corrected. A new argument for the location $z_c$ of the transition is reported in Appendix B.3

References in corpus (11)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Active matter
• Activity-induced phase separation and self-assembly in mixtures of active and passive particles
• Statistical distribution of quantum entanglement for a random bipartite state
• First-passage time of run-and-tumble particles
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Condensation transition in joint large deviations of linear statistics
• Participation ratio for constraint-driven condensation with superextensive mass
• Conditioned random walks and interaction-driven condensation

Cited by in corpus (56)

• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Long time position distribution of an active Brownian particle in two dimensions
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• Statistical Mechanics of Systems with Negative Temperature
• The Parental Active Model: a unifying stochastic description of self-propulsion
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Occupation time of a run-and-tumble particle with resetting
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Collective motion in large deviations of active particles
• Velocity and diffusion constant of an active particle in a one dimensional force field
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Transport in disordered systems: the single big jump approach
• Survival probability of a run-and-tumble particle in the presence of a drift
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Mean area of the convex hull of a run and tumble particle in two dimensions
• Hard core run and tumble particles on a one dimensional lattice
• Tracer dynamics in one dimensional gases of active or passive particles
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Giant leaps and long excursions: fluctuation mechanisms in systems with long-range memory
• Run-and-Tumble particle in inhomogeneous media in one dimension
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Entropy production and its large deviations in an active lattice gas
• Local time for run and tumble particle
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Work fluctuations of self-propelled particles in the phase separated state
• Current fluctuations in stochastically resetting particle systems
• Rare events in stochastic processes with sub-exponential distributions and the Big Jump principle
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Encounter-based model of a run-and-tumble particle
• Thermodynamic uncertainty for run-and-tumble type processes
• Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• A large deviation perspective on ratio observables in reset processes: robustness of rate functions
• Active Random Walks in One and Two Dimensions
• Finite-size localization scenarios in condensation transitions
• Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model
• Probability distributions with singularities
• Generating constrained run-and-tumble trajectories
• Local time of a system of Brownian particles on the line with steplike initial condition
• Beat of a current
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Rare Events and Single Big Jump Effects in Ornstein-Uhlenbeck Processes
• Nonlinear-Cost Random Walk: exact statistics of the distance covered for fixed budget
• Fluctuation Theorems for Heat exchanges between passive and active baths
• Data-driven analysis of annual rain distributions
• Beyond the Big Jump: A Perturbative Approach to Stretched-Exponential Processes
• Work fluctuations for a confined Brownian particle: the role of initial conditions
• Anatomy of an extreme event: What can we infer about the history of a heavy-tailed random walk?
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Extreme value statistics in a continuous time branching process: a pedagogical primer
• Morphology, Polarization Patterns, Compression, and Entropy Production in Phase-Separating Active Dumbbell Systems
• Mapping current and activity fluctuations in exclusion processes: consequences and open questions