Asymmetric stochastic resetting: Modeling catastrophic events

Plata, Carlos A.; Gupta, Deepak; Azaele, Sandro

doi:10.1103/physreve.102.052116

Cited by 24 publications

(17 citation statements)

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“…(•) In quantitative financial mathematics, the models of option pricing for barrier-type and reset-type options (involving option-price adjustments upon crossing certain price boundaries or at preset dates during its life-time) are known for decades [117][118][119][120][121] . Abrupt drops of stock-market prices at times of economic crashes and other sudden catastrophic events 60 can also be viewed as reset-related phenomena. (•) Recent experimental (wo-)man-made particletracking resetting setups involve a manipulation of micron-sized beads in optical traps 122 and "tweezers" 66,67 and can potentially yield time series amenable for a single-trajectory-based time-averaging analysis to decipher the underlying diffusion process, as in the theory developed below.…”

Section: B Some Examples Of Resettingmentioning

confidence: 99%

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

et al. 2021

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How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD-and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0|x| γ , and of their "combined" process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle' displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for "confined" processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

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Section: B Some Examples Of Resettingmentioning

confidence: 99%

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

et al. 2021

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Section: B Some Examples Of Resettingmentioning

confidence: 99%

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Wang

Cherstvy

Kantz

et al. 2021

Preprint

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How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does the process of stochastic resetting impact nonergodicity? These are the main questions addressed in this study. Specifically, we examine, both analytically and by stochastic simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of fractional Brownian motion (FBM) with a long-time memory, of heterogeneous diffusion processes (HDPs) with a power-law-like space-dependent diffusivity D(x) = D0|x|γ and of their "combined" process of HDP-FBM. We find, i.a., that the resetting dynamics of originally ergodic FBM for superdiffusive choices of the Hurst exponent develops distinct disparities in the scaling behavior and magnitudes of the MSDs and mean TAMSDs, indicating so-called weak ergodicity breaking (WEB). For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD, and additionally observe a new trimodal form of the probability density function (PDF) of particle' displacements. For all three reset processes (FBM, HDPs, and HDP-FBM) we compute analytically and verify by stochastic computer simulations the short-time (normal and anomalous) MSD and TAMSD asymptotes (making conclusions about WEB) as well as the long-time MSD and TAMSD plateaus, reminiscent of those for "confined" processes. We show that certain characteristics of the reset processes studied are functionally similar, despite the very different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity breaking parameter EB as a function of the resetting rate r. For all the reset processes studied, we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB~ (1/r)-decay at large r values. Together with the emerging MSD-versus-TAMSD disparity, this pronounced r-dependence of the EB parameter can be an experimentally testable prediction. We conclude via discussing some implications of our results to experimental systems featuring resetting dynamics.

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“…Stochastic resetting exhibits remarkable theoretical properties that have made the former an excellent tool to analyze non-equilibrium stationary states [2][3][4][5], thermodynamic speed limit [6], thermodynamic uncertainty relation [7], inducing and optimizing the Markovian Mpemba effect [8], antiviral therapies [9], modeling cell division [10], survival in an unstable system [11], tax dynamics [12], just to cite a few hot topics in non-equilibrium statistical mechanics assisted by stochastic resetting. However, it is not only in the theoretical perspective that stochastic resetting becomes popular, there are certainly a myriad of applications, from search and foraging processes [1,[13][14][15] to ecological disasters [16] passing though enzymatic reactions [17], see [18] for a thorough review.…”

Section: Introductionmentioning

confidence: 99%

Work fluctuations for diffusion dynamics submitted to stochastic return

Gupta

Plata

2022

New J. Phys.

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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.

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Asymmetric stochastic resetting: Modeling catastrophic events

Cited by 24 publications

References 50 publications

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Time-averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

Work fluctuations for diffusion dynamics submitted to stochastic return

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