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Symmetric Exclusion Process under Stochastic Resetting
Statistical Mechanics · Submitted 27 Jun 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly.
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We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current and the total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. | contribution 0.96 | 0.93 | 0.44 | asserted 1.00 |
| s1 | We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration and is strongly correlated to the diffusive current. | result 0.95 | 0.97 | 0.37 | asserted 1.00 |
| s2 | We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current and the total current (sum of the diffusive and the resetting currents) using the renewal approach. | result 0.92 | 0.96 | 0.12 | asserted 1.00 |
| s3 | We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour. | result 1.00 | 0.95 | 0.16 | asserted 1.00 |
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Original abstract
We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current and the total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour.
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4 arXiv papers cite this in 4 sentences
Papers citing it
Cites it as background 4 papers
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This model has led to a large volume of work covering diffusion with resetting in the presence of a potential field [ref] , in different geometrical confinements [ref] , in higher dimensions [ref] , with non-Poissonian resetting protocols [ref] , with interactions [ref] , and more.
Invariants of motion with stochastic resetting and space-time coupled returns · Introduction · 0.90
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The simple model of diffusion with stochastic resetting has been extended and generalized to cover: diffusion in the presence of a potential [ref] , in a domain [ref] , and arbitrary dimensions [ref] ; diffusion in the presence of non-exponential resetting time distributions e.g., deterministic [ref] , intermittent [ref] , non-Markovian [ref] , non-stationary [ref] , with general time dependent resetting rates [ref] , as well as other protocols [ref] ; and diffusion in the presence of interactions [ref] .
Diffusion with stochastic resetting is invariant to return speed · Introduction · 0.86
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Counting statistics are relevant in classical physics, for instance, when studying transport problems [ref] and were thoroughly studied for diffusive systems [ref] , particles with resetting [ref] , active lattice gases [ref] , run and tumble particles [ref] , and exclusion processes [ref] .
Importance Sampling for counting statistics in one-dimensional systems · Introduction · 0.91
What it cites
Cites as background 1 paper
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Several variations and extensions of this simple model have been explored in recent years [ref] .
Search with home returns provides advantage under high uncertainty · Introduction · 0.86
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