Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model

Abstract

We study the large deviations of the power injected by the active force for an Active Ornstein-Uhlenbeck Particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by it a) direct sampling of the active work in numerical solutions of the AOUP equations and b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods a) and b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.

arXiv comment33 pages, 12 figures

References in corpus (62)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Mechanics and Statistics of Active Matter
• The large deviation approach to statistical mechanics
• Motility-Induced Phase Separation
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Fluctuation theorem for stochastic dynamics
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• Dynamical ensembles in stationary states
• Motility-driven glass and jamming transitions in biological tissues
• How far from equilibrium is active matter?
• Swarming and swirling in self-propelled polar granular rods
• Large-scale collective properties of self-propelled rods
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Full phase diagram of active Brownian disks: from melting to motility-induced phase separation
• Thermodynamic formalism for systems with Markov dynamics
• Direct evaluation of large-deviation functions
• A self-propelled particle in an external potential: is there an effective temperature?
• The effective temperature
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Irreversibility in active matter systems: Fluctuation theorem and mutual information
• Dynamics of a self-propelled particle in a harmonic trap
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Entropy production and fluctuation theorems for active matter
• Hidden entropy production and work fluctuations in an ideal active gas
• Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System
• Entropy production of active particles and for particles in active baths
• Injected Power Fluctuations in Langevin Equation
• Inertial self-propelled particles
• Directed transport of active particles over asymmetric energy barriers
• Current fluctuations in the zero-range process with open boundaries
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Population dynamics method with a multi-canonical feedback control
• The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
• Steady State of an Active Brownian Particle in Two-Dimensional Harmonic Trap
• Optimizing active work: Dynamical phase transitions, collective motion, and jamming
• A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle
• Large fluctuations and dynamic phase transition in a system of self-propelled particles
• Long time position distribution of an active Brownian particle in two dimensions
• Phase co-existence in bidimensional passive and active dumbbell systems
• Phase separation and large deviations of lattice active matter
• Constraint driven condensation in large fluctuations of linear statistics
• Thermodynamic cycles with active matter
• Entropy production fluctuations encode collective behavior in active matter
• Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
• How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Dynamics of a homogeneous active dumbbell system
• Collective motion in large deviations of active particles
• Condensation of Fluctuations in and out of Equilibrium
• Simulation of large deviation functions using population dynamics
• Work fluctuations of self-propelled particles in the phase separated state
• Efficiency of one-dimensional active transport conditioned on motility
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• Path probability of stochastic motion: A functional approach
• Fluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter

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• Entropy production of active Brownian particles going from liquid to hexatic and solid phases
• Optimal run-and-tumble in slit-like confinement
• Fluctuation Theorems for Heat exchanges between passive and active baths
• Confined active particles with spatially dependent Lorentz force: an odd twist to the "best Fokker-Planck approximation"
• Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation
• Work fluctuations for a confined Brownian particle: the role of initial conditions