{
  "abstract": "We introduce a unified optimal transport framework for the Immersed Boundary (IB) electrodiffusion active pump model. By representing membrane chemical potential barriers and active pump potentials via smoothed Eulerian kernels ($Ψ_w, \\mathcal{H}_w$), we formulate the passive dynamics as an $L^2$-Wasserstein ($W_2$) gradient flow coupled to non-conservative active pushing fields representing ATP-driven $3:2$ $\\text{Na}^+/\\text{K}^+$ exchangers. We establish global weak existence of solutions to the continuous Poisson--Nernst--Planck--IB system via a split-step Jordan--Kinderlehrer--Otto (JKO) variational scheme, backed by Calderón--Zygmund bounds for non-local Poisson drift and $H^3(\\mathbb{S}^1)$ interface regularity under Stokes flow. We prove the continuous Rayleighian energy balance and establish exponential $W_2$-stability of Non-Equilibrium Steady States (NESS) under a quantitative Bakry--Émery curvature threshold. Furthermore, we analyze the dual singular limits of kernel smoothing width $w \\to 0$ and dimensionless Debye length $g = λ_D / L \\to 0$. We establish the precise asymptotic regime connecting regularized and sharp models, prove the $Γ$-convergence of regularized energy functionals, derive distributional interface flux jump conditions, and resolve $O(λ_D)$ Debye space-charge boundary layers to confirm bulk electroneutrality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40942",
  "author_total": 1,
  "authors": [
    {
      "name": "Pilhwa Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/11qhaxfqe5c93.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40942",
  "fulltext_url": null,
  "id": "11qhaxfqe5c93",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40942",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "q-bio.CB"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/11qhaxfqe5c93.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40942"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.CB",
      "subfield": "cell-biology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Immersed Boundary Electrodiffusion in the Wasserstein Gradient Flow Formalism: Global Well-Posedness, Non-Equilibrium Thermodynamics, and Singular Asymptotics",
  "title_text": "Immersed Boundary Electrodiffusion in the Wasserstein Gradient Flow Formalism: Global Well-Posedness, Non-Equilibrium Thermodynamics, and Singular Asymptotics",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/11qhaxfqe5c93",
  "venue": "arXiv",
  "versions": []
}