Work fluctuations for diffusion dynamics submitted to stochastic return

Abstract

Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to determine the work distribution for returning a system facilitated by a confining potential with its minimum at the restart location. The general strategy, based on average over \textit{resetting pathways}, constitutes a robust method to gain access to the statistical information of observables from resetting systems. We exploit paradigmatic setups, where explicit computations are attainable, to illustrate the theory. Numerical simulations validate our theoretical predictions. For some of these examples, a non-trivial behavior of the work fluctuations opens a door to optimization problems. Specifically, work fluctuations can be minimized by an appropriate tuning of the return rate.

Optimal resetting strategies for search processes in heterogeneous environments

“…We have focused on providing a minimal model, for which the novel first passage properties stemming from the disorder could be obtained in an exact way. However, there are many aspects still to be explored, as a consequence of the distributed target position: (i) the latter can be interpreted as a quenched disorder, and a search process in a quenched vs annealed case can be investigated in the framework of disordered systems [18,36,37]; (ii) the problem of finding an optimal resetting rate α(x) for a given target distribution p T (x T ) in 1d processes is still open [1,33], and our work represents a first step in this direction; (iii) our results may be generalised to higher-dimensional systems, where we conjecture that the MFPT performance may increase significantly [38]; (iv) prior information about the target distribution leads to more efficient search strategies; in the context of stochastic thermodynamics [39][40][41], it would be interesting to address the role of fluctuation relations and the entropy of information in resetting systems [42][43][44]-in analogy with the situation found in feedback controlled systems [45][46][47]; (v) it is tempting to associate this information to an active particle exploring the environment with a persistent self-propulsion [48,49], following recent approaches in resetting dynamics [50,51]. (s|x 0 ) yields…”

Stochastic resetting with refractory periods: pathway formulation and exact results

“…On the one hand, it has been successfully used in many different applications, ranging from economics [8][9][10][11][12][13][14] to biochemical reactions [15][16][17][18][19] or ecology [20][21][22][23], mostly motivated by the beneficial effect of restart for lowering the first passage time [1,2,[24][25][26][27][28][29]. On the other hand, it constitutes an excellent test bench for performing non-equilibrium research, providing comprehensive models to study non-equilibrium steady states (NESS) [30][31][32][33][34][35][36][37], stochastic thermodynamics and fluctuation theorems [17,[38][39][40][41][42], large deviations [43][44][45][46][47][48], or quantum restart [49][50][51]…”

“…Depending on the phenomena, different strategies-mainly, the insertion of new phases-have been proposed to tackle this flaw in the simplest resetting model. On the one hand, return phases that alternate with the natural dynamics have been introduced [37,42,[55][56][57][58][59]. On the other hand, a motionless phase [60,61], termed as refractory period, may be introduced after the resetting, which can be envisioned as a recovery time payed after performing the reset.…”

On a diffusion which stochastically restarts from moving random spatial positions: a non-renewal framework

“…However, dropping out some of the assumptions surrounding the motion of a resetting Brownian particle leads to many generalizations of Evans-Majumdar process. Thus intensive research has been done to deal with models where motion remains confined to bounded domains [37][38][39][40][41], particles are subjected to potential fields [8,14,[42][43][44][45][46][47][48][49][50][51], time intervals between resets follow power-law distributions instead of being exponentially distributed [52], resetting rate is time-dependent [53], resettings are non-instantaneous [54][55][56], diffusion takes place on comb structures [57][58][59].…”