Stochastic resetting in interacting particle systems: a review

Nagar, Apoorva; Gupta, Shamik

doi:10.1088/1751-8121/acda6c

Cited by 20 publications

(7 citation statements)

References 78 publications

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“…(2 √ 2rτ ) −1 (see equation ( 169)) allows to recover the result reported in equation (33). Substituting into equation (94) yields the equivalents…”

Section: Average Opinion Statementioning

confidence: 61%

“…Global resetting has also been studied for exclusion processes [20][21][22], as well as predatorprey models [23][24][25], fluctuating interfaces [26,27], synchronization [28], reaction-diffusion processes [29], glassy systems [30] and zero-range processes [31,32]. For a review of developments on interacting particle systems under stochastic resetting, see [33] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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Voter model under stochastic resetting

Grange

2023

J. Phys. A: Math. Theor.

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The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each voter flips randomly, at a rate proportional to the fraction of the nearest neighbors that disagree with the voter. If the voters are initially independent and undecided, the model is known to lead to a consensus if and only if $d\leq 2$. In this paper the model is subjected to stochastic resetting: the voters revert independently to their initial opinion according to a Poisson process of fixed intensity (the resetting rate). This resetting prescription induces kinetic equations for the average opinion state and for the two-point function of the model. For initial conditions consisting of undecided voters except for one decided voter at the origin, the one-point function evolves as the probability of presence of a diffusive random walker on the lattice, whose position is stochastically reset to the origin. The resetting prescription leads to a non-equilibrium steady state. For an initial state consisting of independent undecided voters, the density of domain walls in the steady state is expressed in closed form as a function of the resetting rate. This function is differentiable at zero if and only if $d\geq 5$.

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“…(2 √ 2rτ ) −1 (see equation ( 169)) allows to recover the result reported in equation (33). Substituting into equation (94) yields the equivalents…”

Section: Average Opinion Statementioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Voter model under stochastic resetting

Grange

2023

J. Phys. A: Math. Theor.

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“…It would also be interesting to carry out a deeper investigation about the random motion of shocks in the crossover regime, possibly developing an ad-hoc theory based on a Fokker-Planck equation, along the lines of [16,45]. Furthermore, one could investigate to what extent the observed phenomena can be affected by any concurrent processes, such as Langmuir kinetics [23,37] or local stochastic resetting [46][47][48][49], or eventually by resource constraints [50][51][52]. We are considering these types of questions as possible topics for future work.…”

Section: Discussionmentioning

confidence: 99%

Interaction vs inhomogeneity in a periodic TASEP

Mina,

Paninforni,

Pelizzola

et al. 2024

J. Phys. A: Math. Theor.

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We study the non-equilibrium steady states in a totally-asymmetric simple-exclusion process with periodic boundary conditions, also incorporating (i) an extra (nearest-neighbour) repulsive interaction and (ii) hopping rates characterized by a smooth spatial inhomogeneity. We make use of a generalized mean-ﬁeld approach (at the level of nearest-neighbour pair clusters), in combination with kinetic Monte Carlo simulations. It turns out that the so-called shock phase can exhibit a lot of qualitatively diﬀerent subphases, including multiple-shock phases, and a minimal-current shock phase. We argue that the resulting, considerably rich phase diagram should be relatively insensitive to minor details of either interaction or spatial inhomogeneity. As a consequence, we also expect that our results help elucidate the nature of shock subphases detected in previous studies.

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“…In this paper, the boundary walls perform free diffusion with Poisson resetting where the waiting time between the two resetting events is drawn from an exponential distribution. However, the dynamics of the boundary walls can be generalized where the waiting time between two consecutive resetting events follow a power-law distribution [34,59,60] or the resetting mechanism becomes non-instantaneous [45,[61][62][63]. It is expected that such changes in the dynamics of the boundary walls will affect the NESS of the ordered harmonic chain and it is intriguing to explore the transport properties of such NESS.…”

Section: Discussionmentioning

confidence: 99%

Stationary state of harmonic chains driven by boundary resetting

Sarkar,

Roy

2023

J. Stat. Mech.

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We study the nonequilibrium steady state of an ordered harmonic chain of N oscillators connected to two walls which undergo diffusive motion with stochastic resetting. The intermittent resetting of the walls effectively emulates two nonequilibrium reservoirs that exert temporally correlated forces on the boundary oscillators. These reservoirs are characterized by the diffusion constants and resetting rates of the walls. We find that, for any finite N, the velocity distribution of the bulk oscillators remains non-Gaussian, as evidenced by a non-zero bulk kurtosis that decays ∼ N − 1 . We calculate the spatio-temporal correlation of the velocity of the oscillators ⟨ v l ( t ) v l ′ ( t ′ ) ⟩ both analytically as well as using numerical simulation. The signature of the boundary resetting is present at the bulk in terms of the two-time velocity correlation of a single oscillator and the equal-time spatial velocity correlation. For the resetting driven chain, the two-time velocity correlation decay as t − 1 2 at the large time, and there exists a non-zero equal-time spatial velocity correlation ⟨ v l ( t ) v l ′ ( t ′ ) ⟩ when l ≠ l ′ . A non-zero average energy current will flow through the system when the boundary walls reset to their initial positions at different rates. This average energy current can be computed exactly in the thermodynamic limit. Numerically we show that the distribution of the instantaneous energy current at the boundary is independent of the system size. However, the distribution of the instantaneous energy current in the bulk approaches a stationary distribution in the thermodynamic limit.

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Stochastic resetting in interacting particle systems: a review

Cited by 20 publications

References 78 publications

Voter model under stochastic resetting

Voter model under stochastic resetting

Interaction vs inhomogeneity in a periodic TASEP

Stationary state of harmonic chains driven by boundary resetting

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