{
  "abstract": "We study the emergence of non-equilibrium steady states (NESS) in stochastic processes under threshold resetting, an event-driven protocol in which the system resets to its initial configuration upon crossing a prescribed spatial boundary (threshold). In contrast to externally driven resetting, whose steady-state properties are well understood, the behavior under threshold resetting remains largely unexplored. We derive general conditions for the existence of a NESS and show that, whenever it exists, the steady state at a given position $x$ can be expressed as the ratio of two fundamental quantities: the mean local time (MLT) at $x$ and the mean first-passage time (MFPT) to hit the threshold. In particular, for noisy systems, a finite MFPT guarantees the existence of a NESS. As an illustrative example, we analyze a drift-diffusion process in one dimension and uncover rich intermediate-time dynamics, including anomalous relaxation in the spatial distribution, damped oscillations in the moments and in the mean-squared displacement (MSD), governed by system parameters. Our findings provide a general understanding of the emergence of non-equilibrium steady states and relaxation dynamics under threshold resetting, revealing how induced events shape the spatial and temporal properties of a broad class of stochastic processes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24438",
  "author_total": 3,
  "authors": [
    {
      "name": "Rahul Das"
    },
    {
      "name": "Satya N Majumdar"
    },
    {
      "name": "Arnab Pal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxkkzkgv8ppnw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24438",
  "fulltext_url": null,
  "id": "fxkkzkgv8ppnw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24438",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7214017548",
  "pdf_url": "https://arxiv.org/pdf/2609.24438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxkkzkgv8ppnw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24438"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Non-equilibrium dynamics of drift-diffusion process under threshold resetting",
  "title_text": "Non-equilibrium dynamics of drift-diffusion process under threshold resetting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/fxkkzkgv8ppnw",
  "venue": "arXiv",
  "versions": []
}