{
  "abstract": "The Redfield equation with time-dependent coefficients (or TCL2 equation) gives one of the simplest perturbative descriptions of open quantum system dynamics derived from a microscopic theory. Its status as an approximation is nevertheless subtle: while perturbation theory fixes the reduced dynamics order-by-order in the system-environment coupling, solving the Redfield equation yields a particular resummation that need not preserve complete positivity. Here we compare Redfield evolution with an exponentiated (Magnus) resummation of the same second-order perturbative map, which is completely positive and trace preserving (CPTP) for a broad class of physical conditions. We also construct a simple CPTP resolvent resummation, illustrating the non-uniqueness of resummations of the same perturbative map. The Redfield and Magnus prescriptions agree to second order but differ through time-ordering corrections at higher orders. We exhibit a weak-coupling criterion which guarantees that Redfield evolution, even when non-Markovian, remains close to a CPTP map. We illustrate the criterion in two examples, focusing on finite-dimensional (qubit) systems. Our results clarify when, and why, Redfield evolution can remain reliable even when it is highly non-Lindbladian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03676",
  "author_total": 2,
  "authors": [
    {
      "name": "Greg Kaplanek"
    },
    {
      "name": "Jason Pollack"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6n3zhvkm8dpe5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03676",
  "fulltext_url": null,
  "id": "6n3zhvkm8dpe5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03676",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7220386858",
  "pdf_url": "https://arxiv.org/pdf/2610.03676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6n3zhvkm8dpe5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03676"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "How I Learned to Stop Worrying and Love the Redfield Equation: Completely-Positive Resummation of Non-Markovian Dynamics",
  "title_text": "How I Learned to Stop Worrying and Love the Redfield Equation: Completely-Positive Resummation of Non-Markovian Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/6n3zhvkm8dpe5",
  "venue": "arXiv",
  "versions": []
}