Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems

Abstract

We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles, respectively. We derive analytic results for the fluctuations in the number of particles exiting the boundaries of the finite confining box. The statistical properties of this quantity crucially depend on how the system is prepared initially. Two common types of averages employed to understand the impact of initial conditions in stochastic systems are annealed and quenched averages. It is well known that for an infinitely extended system, these different initial conditions produce quantitatively different fluctuations, even in the infinite time limit. We demonstrate explicitly that in finite systems, annealed and quenched fluctuations become equal beyond a system-size dependent timescale, $t\sim L^2$. For diffusing particles, the fluctuations exhibit a $\sqrt{t}$ growth at short times and decay as $1/\sqrt{t}$ for time scales, $t\gg L^2/D$, where $D$ is the diffusion constant. Meanwhile, for run-and-tumble particles, the fluctuations grow linearly at short times and then decay as $1/\sqrt{t}$ for time scales, $t\gg L^2/D_{\text{eff}}$, where $D_{\text{eff}}$ represents the effective diffusive constant for run-and-tumble particles. To study the effect of confinement in detail, we also analyze two different setups (i) with one reflecting boundary and (ii) with both boundaries open.

15 pages, 8 figures

References in corpus (40)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Macroscopic current fluctuations in stochastic lattice gases
• Run and tumble particle under resetting: a renewal approach
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Stochastic interacting particle systems out of equilibrium
• Non equilibrium current fluctuations in stochastic lattice gases
• Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem
• Large Deviations in Single File Diffusion
• First passages for a search by a swarm of independent random searchers
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Entropic particle transport in periodic channels
• Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
• First-passage time of run-and-tumble particles
• Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• The Lasting Effect of Initial Conditions on Single File Diffusion
• Phase Transition in the ABC Model
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• From interacting particle systems to random matrices
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• Dynamical fluctuations in the Riesz gas
• Intrinsic fractional noise in nanopores: The effect of reservoirs
• Phase fluctuations in the ABC model
• Current fluctuations in stochastically resetting particle systems
• Effusion of stochastic processes on a line
• Current fluctuations in an interacting active lattice gas
• Tagged particle in single-file diffusion with arbitrary initial conditions
• Generalized disorder averages and current fluctuations in run and tumble particles
• Active Random Walks in One and Two Dimensions
• First passage statistics of active random walks on one and two dimensional lattices
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• Chiral run-and-tumble walker: transport and optimizing search