{
  "abstract": "Two canonical preparations evolving under a common final Markov generator can exhibit the Mpemba effect because they excite different relaxation modes. We bound the first crossing of their relative entropies by treating relaxation as an entropy-production race. The exact balance $-\\dot D=\\dot e_p$ implies that a meeting occurs when the accumulated \\emph{difference} of normalized entropy-production rates, $\\int_0^t(r_H-r_C)\\,\\mathrm ds$ with $r_α=\\dot e_p^α/D_α$, equals the initial logarithmic deficit $\\ln[D_H(0)/D_C(0)]$. Global entropy-decay inequalities yield a lower crossing-time bound when the entropy-decay constant is bounded from below and the hot rate from above; we supply both certificates. A nonzero cubic moment of a slowest eigenfunction is sufficient for the modified logarithmic Sobolev constant to lie strictly below the spectral gap. Combining established relative-entropy comparison inequalities with Markov contraction and the actual mode amplitudes gives finite-amplitude crossing bounds without a small-deviation expansion. For an exactly strong, reversible three-state preparation these give $0.1659\\le t_M\\le0.1674$ in model time units, independently certified by outward-rounded interval arithmetic. This interval is narrower than $1\\%$ and contains $t_M=0.1662209$. The conservative global-rate comparison used here gives only $t_M\\ge0.042$. The hotter preparation starts $6.12$ times farther from equilibrium, yet it reaches $D=10^{-5}$ at $t=0.233$, compared with $t=0.844$ for the colder one. Mean energy crosses later than relative entropy. For a fixed driven generator, nonadiabatic entropy production governs the same balance. These results concern finite-state relaxation in a specified distance and do not predict water-freezing times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40704",
  "author_total": 1,
  "authors": [
    {
      "name": "Mesfin Taye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv9vpe8kvxt81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40704",
  "fulltext_url": null,
  "id": "dv9vpe8kvxt81",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40704",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dv9vpe8kvxt81.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.40704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40704"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Mpemba effect as an entropy-production race:Finite-amplitude bounds on crossing times in Markovian relaxation",
  "title_text": "Mpemba effect as an entropy-production race:Finite-amplitude bounds on crossing times in Markovian relaxation",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/dv9vpe8kvxt81",
  "venue": "arXiv",
  "versions": []
}