The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. Here, we bridge this gap by developing a microscopic theory of adsorption kinetics, from which the macroscopic properties follow directly. One of our central achievements is the derivation of a microscopic version of the seminal Ward–Tordai relation, and its generalization to arbitrary dimension, geometry, and initial conditions.

We generalize the model of diffusion with resetting to account for situations where a particle is returned only a fraction of its distance to the origin, e.g., half way. We show that this model always attains a steady-state distribution which can be written as an infinite sum of independent, but not identical, Laplace random variables. As a result, we find that the steady-state transitions from the known Laplace form which is obtained in the limit of full resetting to a Gaussian form which is obtained close to the limit of no resetting. 

Restart has the potential of expediting or impeding the completion times of general random processes. Consequently, the issue of mean-performance takes center stage: quantifying how the application of restart on a process of interest impacts its completion-time's mean. Going beyond the mean, little is known on how restart affects stochasticity measures of the completion time. We present a comprehensive analysis that quantifies how sharp restart—a keystone restart protocol—impacts the the entropy and diversity of the completion time.

We demonstrate how service resetting can dramatically lower waiting times and improve overall performance of queueing systems (natural and man-made). Random service time fluctuations are notorious for causing major backlogs and delays in such systems. Yet, we show that when these fluctuations are intrinsic to the server—a remarkably simple service resetting protocol can reverse their deleterious effects and significantly cut down queues and waits.   

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We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. We employ resetting for enhanced sampling of molecular simulations for the first time, and show that it accelerates long time scale processes by up to an order of magnitude in examples ranging from simple models to a molecular system. Most importantly, we recover the mean transition time without resetting, which is typically too long to be sampled directly, from accelerated simulations at a single restart rate.

Shlomi Reuveni speaks at the Statistical Physics and Complexity Webinar Series, School of Physics and Astronomy, The University of Edinburgh, April 19, 2022.