{
  "abstract": "We study a dynamical optimal transport problem on path-space with kinetic cost and nonlocal interaction. For a Gaussian interaction kernel, cyclical monotonicity and the regularity of the effective endpoint cost yield a conservative vector field associated with the initial momentum of the optimal trajectories. Separately, the Gaussian interaction potential $W_{π_0}$ satisfies a uniform gradient estimate and, under a quantitative condition on the interaction strength, is a classical and hence viscosity subsolution of an eikonal equation. We also derive the Euler--Lagrange dynamics directly from path-space optimality by means of endpoint-preserving perturbations of the optimal path measure. The associated phase-space marginals satisfy a measure-valued Liouville-type, or nonlocal kinetic, equation driven by the smooth Gaussian self-consistent force. Conversely, a superposition principle lifts suitable measure-valued solutions of the phase-space continuity equation to measures on phase-space trajectories. Thus path-space optimal transport provides a variational connection between endpoint geometry, eikonal behavior of the Gaussian interaction potential, and kinetic mean-field dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05754",
  "author_total": 1,
  "authors": [
    {
      "name": "Rene Cabrera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgakqtabd3q15.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05754",
  "fulltext_url": null,
  "id": "bgakqtabd3q15",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05754",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220706907",
  "pdf_url": "https://arxiv.org/pdf/2610.05754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgakqtabd3q15.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Path-Space Optimal Transport with Interactions: Kinetic Equations and Eikonal Structure",
  "title_text": "Path-Space Optimal Transport with Interactions: Kinetic Equations and Eikonal Structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/bgakqtabd3q15",
  "venue": "arXiv",
  "versions": []
}