Stochastic Resetting vs. Thermal Equilibration: Faster Relaxation, Different Destination

Abstract

Stochastic resetting is known for its ability to accelerate search processes and induce non-equilibrium steady states. Here, we compare the relaxation times and resulting steady states of resetting and thermal relaxation for Brownian motion in a harmonic potential. We show that resetting always converges faster than thermal equilibration, but to a different steady-state. The acceleration and the shape of the steady-state are governed by a single dimensionless parameter that depends on the resetting rate, the viscosity, and the stiffness of the potential. We observe a trade-off between relaxation speed and the extent of spatial exploration as a function of this dimensionless parameter. Moreover, resetting relaxes faster even when resetting to positions arbitrarily far from the potential minimum.