  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.
