Current fluctuations in finite-sized passive and active systems

We investigate the problem of effusion of particles initially confined in a finite one-dimensional box. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles respectively. Two common types of averages employed to understand the effect of initial conditions in such 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. Our exact results reveal how slight variations in the initial conditions as well as different boundary conditions can affect transport properties of stochastic systems.

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