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arxiv: 2604.01986 · v2 · submitted 2026-04-02 · ❄️ cond-mat.stat-mech · cond-mat.soft· math.PR· physics.chem-ph

Resetting optimized competitive first-passage outcomes in non-Markovian systems

Suvam Pal , Rahul Das , Arnab Pal This is my paper

Pith reviewed 2026-05-13 20:58 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.softmath.PRphysics.chem-ph
keywords stochastic resettingnon-Markovian systemsfirst-passage timescontinuous-time random walkfluctuationscompeting outcomesmemory effects
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The pith

Stochastic resetting suppresses fluctuations in conditional first-passage times of non-Markovian systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies the effects of stochastic resetting on first-passage processes involving multiple competing outcomes in systems with memory, modeled using continuous-time random walks. It demonstrates that resetting can enhance the likelihood of preferred outcomes and derives an inequality showing how it reduces variability in the times to those outcomes, with the suppression depending on the waiting time distribution. Readers would care because non-Markovian effects are prevalent in real systems like molecular diffusion in crowded environments, and resetting offers a way to control them beyond simple memoryless cases.

Core claim

Using the continuous-time random walk framework, the authors show that stochastic resetting in non-Markovian systems with competing first-passage outcomes leads to selective enhancement of desired events and an inequality that quantifies the reduction in fluctuations of conditional first-passage times, revealing regimes of significant variability suppression sensitive to waiting-time statistics.

What carries the argument

The inequality quantifying resetting's control over fluctuations in conditional first-passage times.

Load-bearing premise

The continuous-time random walk framework with chosen waiting-time distributions sufficiently captures the memory effects arising from slow relaxation, rugged landscapes, and crowding in the systems studied.

What would settle it

Observing that resetting increases rather than suppresses fluctuations in conditional first-passage times for a system whose waiting times match those assumed in the model.

Figures

Figures reproduced from arXiv: 2604.01986 by Arnab Pal, Rahul Das, Suvam Pal.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic representation of the CTRW in a one [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Variation of the conditional MFPTs with resetting [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Illustration of the system-parameter domains ob [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time random walk (CTRW) framework, we analyze first-passage processes with multiple competing outcomes and examine how resetting can selectively enhance desired events. We characterize the efficiency of resetting through conditional mean first-passage times (MFPTs) and demonstrate that its impact is highly sensitive to the underlying waiting-time statistics. Furthermore, we derive an inequality that quantifies how resetting controls fluctuations in conditional first-passage times (FPTs), revealing regimes where variability is significantly suppressed. Our results provide a systematic understanding of how long-term memory influences competitive first-passage outcomes and establish resetting as a powerful control mechanism beyond the conventional Markovian setting.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses the continuous-time random walk (CTRW) framework to study stochastic resetting in non-Markovian systems with competing first-passage outcomes. It characterizes the effect of Poisson resetting on conditional mean first-passage times (MFPTs), demonstrates sensitivity to the underlying waiting-time distribution (power-law and stretched-exponential families), and derives an inequality that bounds the suppression of fluctuations in conditional first-passage times (FPTs) via a variance inequality applied to the Laplace-domain mixture distributions.

Significance. If the inequality holds, the work supplies a concrete, distribution-dependent criterion for when resetting reduces variability in conditional FPTs, extending resetting control beyond Markovian settings to systems with long memory. The formal steps rest on standard CTRW renewal equations and moment inequalities, and the chosen waiting-time families are representative; this combination yields falsifiable predictions for fluctuation suppression that could be tested in single-molecule or disordered-media experiments.

major comments (2)
  1. [§3.2, Eq. (18)] §3.2, Eq. (18): the variance inequality is applied to the conditional FPT mixture after Laplace inversion; the derivation assumes finite second moments of the waiting-time distribution, but the power-law case with exponent 1 < α ≤ 2 has divergent variance, so the claimed suppression bound requires an additional truncation or regularization step that is not stated.
  2. [§4.1, Fig. 3] §4.1, Fig. 3: the numerical demonstration of fluctuation suppression for stretched-exponential waiting times shows a clear minimum versus resetting rate, yet the location of this minimum is not compared against the analytic expression obtained from the inequality; without this comparison the regime of “significant suppression” remains qualitative.
minor comments (2)
  1. [Abstract] The abstract states that resetting “selectively enhance[s] desired events” but does not define the selection criterion; a one-sentence clarification of the figure of merit (e.g., ratio of conditional MFPTs) would help readers.
  2. [§2] Notation for the resetting rate is introduced as r in §2 but appears as γ in several later equations; a single consistent symbol throughout would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which have helped us identify areas for clarification and strengthening. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [§3.2, Eq. (18)] §3.2, Eq. (18): the variance inequality is applied to the conditional FPT mixture after Laplace inversion; the derivation assumes finite second moments of the waiting-time distribution, but the power-law case with exponent 1 < α ≤ 2 has divergent variance, so the claimed suppression bound requires an additional truncation or regularization step that is not stated.

    Authors: We acknowledge the validity of this observation. The derivation of the variance inequality in Eq. (18) does rely on the existence of finite second moments for the waiting-time distribution. For the power-law family with 1 < α ≤ 2, where the variance diverges, the bound cannot be applied directly without regularization. In the revised manuscript we will explicitly state the finite-second-moment assumption in §3.2, introduce a truncation (or cutoff) procedure for the power-law cases to restore finite variance, and derive the corresponding regularized bound. This will be presented as an additional technical step with a brief discussion of its physical motivation. revision: yes

  2. Referee: [§4.1, Fig. 3] §4.1, Fig. 3: the numerical demonstration of fluctuation suppression for stretched-exponential waiting times shows a clear minimum versus resetting rate, yet the location of this minimum is not compared against the analytic expression obtained from the inequality; without this comparison the regime of “significant suppression” remains qualitative.

    Authors: We agree that overlaying the analytic location of the minimum (obtained from the inequality) onto the numerical curves in Fig. 3 would make the demonstration more quantitative. In the revised manuscript we will add this comparison—either by marking the predicted minimum on the figure or by including a short table of analytic versus numerical values—and discuss the degree of agreement. This will allow readers to assess the predictive accuracy of the inequality in the regime of significant suppression. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via CTRW renewal and standard inequalities

full rationale

The central result is an inequality bounding fluctuation suppression in conditional FPTs under resetting. It follows directly from Laplace-domain expressions for the mixture distributions generated by the CTRW renewal equation plus a standard variance inequality applied to those mixtures. No parameter is fitted to the target quantity and then relabeled as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and the waiting-time families are chosen only for illustration after the inequality is already proved. The steps therefore remain independent of the specific numerical outcomes they later illustrate.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the CTRW renewal framework and general waiting-time distributions; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption CTRW with general waiting-time distributions captures non-Markovian memory effects from slow relaxation and crowding
    Invoked to analyze first-passage processes with competing outcomes.

pith-pipeline@v0.9.0 · 5449 in / 1107 out tokens · 36655 ms · 2026-05-13T20:58:10.165798+00:00 · methodology

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Reference graph

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