{
  "abstract": "We develop a variational--Markov construction of detailed-balance master-equation discretizations for Fokker--Planck equations directly from their energy--dissipation laws. Rather than discretizing the differential operator, we represent mass transfer between neighboring grid points by two directional jump rates. On each edge, the discrete energy--dissipation law determines the net flux, while detailed balance fixes the rate ratio; a local reconstruction of edge quantities from neighboring grid-point values then uniquely determines both rates. A logarithmic-mean reconstruction recovers the classical Scharfetter--Gummel/Wang--Peskin--Elston rates, while alternative reconstructions yield other reversible schemes. The resulting semi-discrete systems conserve mass, preserve nonnegativity, satisfy detailed balance, and dissipate a discrete free energy. The same edgewise construction extends to state-dependent and degenerate mobilities, nonlocal interaction energies and higher-dimensional problems. The corresponding implicit and semi-implicit fully discrete schemes are linear, mass-conservative, positivity-preserving, and energy-stable, with a time-step restriction required only for nonlocal interaction energies whose kernel is not negative semidefinite. Numerical experiments confirm the expected spatial convergence rates of all detailed-balance schemes and verify their equilibrium accuracy, positivity preservation, and free-energy decay with discontinuous potentials, saturation, nonlocal interactions, and two-dimensional problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30121",
  "author_total": 2,
  "authors": [
    {
      "name": "Satish Chandran"
    },
    {
      "name": "Yiwei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05xgtwkwdm2r1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30121",
  "fulltext_url": null,
  "id": "05xgtwkwdm2r1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30121",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7204954597",
  "pdf_url": "https://arxiv.org/pdf/2608.30121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05xgtwkwdm2r1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Structure-Preserving Detailed-Balance Master-Equation Discretizations for Fokker--Planck Equations",
  "title_text": "Structure-Preserving Detailed-Balance Master-Equation Discretizations for Fokker--Planck Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/05xgtwkwdm2r1",
  "venue": "arXiv",
  "versions": []
}