Capture of a diffusing lamb by a diffusing lion when both return home

Exact fluctuation and long-range correlations in a single-file model under resetting

Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behavior of a system as exemplified by the emergence of nonequilibrium properties and expedition of search processes. Herein we explore the ramifications of stochastic resetting in the context of a single-file system called random average process (RAP) in one dimension. In particular, we focus on the dynamics of tracer particles and analytically compute the variance, equal time correlation, autocorrelation, and unequal time correlation between the positions of different tracer particles. Our study unveils that resetting gives rise to rather different behaviors depending on whether the particles move symmetrically or asymmetrically. For the asymmetric case, the system for instance exhibits a long-range correlation which is not seen in absence of the resetting. Similarly, in contrast to the reset-free RAP, the variance shows distinct scalings for symmetric and asymmetric cases. While for the symmetric case, it decays (towards its steady value) as ∼e^{-rt}/sqrt[t], we find ∼te^{-rt} decay for the asymmetric case (r being the resetting rate). Finally, we examine the autocorrelation and unequal time correlation in the steady state and demonstrate that they obey interesting scaling forms at late times. All our analytical results are substantiated by extensive numerical simulations.

Efficiency of a microscopic heat engine subjected to stochastic resetting

We explore the thermodynamics of stochastic heat engines in the presence of stochastic resetting. The setup comprises an engine whose working substance is a Brownian particle undergoing overdamped Langevin dynamics in a harmonic potential with a time-dependent stiffness, with the dynamics interrupted at random times with a resetting to a fixed location. The effect of resetting to the potential minimum is shown to enhance the efficiency of the engine, while the output work is shown to have a nonmonotonic dependence on the rate of resetting. The resetting events are found to drive the system out of the linear response regime, even for small differences in the bath temperatures. Shifting the reset point from the potential minimum is observed to reduce the engine efficiency. The experimental setup for the realization of such an engine is briefly discussed.

Bernoulli trial under restarts: A comparative study of resetting transitions

A Bernoulli trial describing the escape behavior of a lamb to a safe haven in pursuit by a lion is studied under restarts. The process ends in two ways: either the lamb makes it to the safe haven (success) or is captured by the lion (failure). We study the first passage properties of this Bernoulli trial and find that only mean first passage time exists. Considering Poisson and sharp resetting, we find that the success probability is a monotonically decreasing function of the restart rate. The mean time, however, exhibits a nonmonotonic dependence on the restart rate taking a minimal value at an optimal restart rate. Furthermore, for sharp restart, the mean time possesses a local and a global minima. As a result, the optimal restart rate exhibits a continuous transition for Poisson resetting while it exhibits a discontinuous transition for sharp resetting as a function of the relative separation of the lion and the lamb. We also find that the distribution of first passage times under sharp resetting exhibits a periodic behavior.