First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions

Abstract

We explore the effects of stochastic resetting to random positions of a Brownian particle on first passage times and Shannon's entropy. We explore the different entropy regimes, namely, the \textit{externally-driven}, the \textit{zero-entropy} and the \textit{Maxwell demon} regimes. We show that the mean first passage time (MPFT) minimum can be found in any of these regimes. We provide a novel analytical method to compute the MFPT, the mean first passage number of resets (MFPNR) and mean first passage entropy (MFPE) in the case where the Brownian particle resets to random positions sampled from a set of distributions known \textit{a priori}. We show the interplay between the reset position distribution's second moment and the reset rate, and the effect it has on the MFPT and MFPE. We further propose a mechanism whereby the entropy per reset can be either in the Maxwell demon or the externally driven regime, yet the overall mean first passage entropy corresponds to the zero-entropy regime. Additionally, we find an overlap between the dynamic phase space and the entropy phase space. We use this method in a generalized version of the Evans-Majumdar model by assuming the reset position is random and sampled from a Gaussian distribution. We then consider the \textit{toggling reset} whereby the Brownian particle resets to a random position sampled from a distribution dependent on the reset parity. All our results are compared to and in agreement with numerical simulations.

arXiv comment12pp, 2SM sections, 7Figs

References in corpus (35)

• Theoretical perspective on the glass transition and amorphous materials
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• High-precision test of Landauer's principle in a feedback trap
• Diffusion with Optimal Resetting
• First Passage Under Restart
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Run and tumble particle under resetting: a renewal approach
• The Energetic Costs of Cellular Computation
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Stochastic resetting in backtrack recovery by RNA polymerases
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Stochastic thermodynamics of resetting
• Energy landscape and rigidity
• Survival of an evasive prey
• Work fluctuations and Jarzynski equality in stochastic resetting
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions
• Transport properties of random walks under stochastic non-instantaneous resetting
• Stochastic resetting in underdamped Brownian motion
• Intermittent resetting potentials
• Diffusive transport on networks with stochastic resetting to multiple nodes
• Lotka-Volterra systems with stochastic resetting
• Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?
• Work fluctuations for diffusion dynamics submitted to stochastic return
• Stochastic resetting antiviral therapies prevents drug resistance development
• The free energy requirements of biological organisms; implications for evolution
• A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
• Predator-prey dynamics: Chasing by stochastic resetting
• Entropy rate of random walks on complex networks under stochastic resetting
• Escape time, relaxation and sticky states of a softened Henon-Heiles model: low-frequency vibrational modes effects

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• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting
• Abrupt transitions in the optimization of diffusion with distributed resetting
• How target distributions shape optimal stochastic resetting
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