Experimental verification of Arcsine laws in mesoscopic non-equilibrium and active systems

TL;DR

This paper experimentally verifies that time-integrated observables in mesoscopic non-equilibrium steady states follow the arcsine laws, revealing how convergence depends on proximity to equilibrium and autocorrelation effects.

Contribution

It demonstrates the applicability of the arcsine laws to mesoscopic non-equilibrium systems and explores how convergence rates vary with system parameters and perturbations.

Findings

Time-integrated observables follow arcsine laws in NESS.

Convergence to arcsine distributions is faster near equilibrium.

System perturbations affect the autocorrelation and convergence rates.

Abstract

A large number of processes in the mesoscopic world occur out of equilibrium, where the time course of a system evolution becomes immensely important since it is driven principally by dissipative effects. Non-equilibrium steady states (NESS) represent a crucial category in such systems, where relaxation timescales are comparable to the operational timescales. In this study, we employ a model NESS stochastic system which comprises of a colloidal microparticle, optically trapped in a viscous fluid, externally driven by a temporally correlated noise, and show that time-integrated observables such as the entropic current, the work done on the system or the work dissipated by it, follow the three Levy arcsine laws [1], in the large time limit. We discover that cumulative distributions converge faster to arcsine distributions when it is near equilibrium and the rate of entropy production is small, because in that case the entropic current has weaker temporal autocorrelation. We study this phenomenon changing the strength of the added noise or by perturbing our system with a flow field produced by a microbubble at close proximity to the trapped particle. We confirm our experimental findings with theoretical simulations of the systems. Our work provides an interesting insight into the NESS statistics of the meso-regime, where stochastic fluctuations play a pivotal role.