{
  "abstract": "We develop a statistical-mechanical theory of water in unsaturated soil whose outcome is a continuum field equation for the pore-occupancy g(r,x,t), the fraction of pores of radius r that are water-filled at position x and time t. The theory is built across three scales: microscopic inter-pore transfers set by Hagen-Poiseuille rates and a driving potential (the difference of pore-class chemical potentials, taken in capillary-gravitational form but open to adsorptive, osmotic, or thermal refinement); a mesoscale master equation relaxing the occupancy toward the equilibrium step g_eq=H(r*-r); and, on contracting the averaging volume to a point, the continuum balance d_t g + div F = C[g] - E - T, of which everything else is a limit, a moment, or a boundary resolution. The kinetic equation is an Onsager gradient flow descending the Gibbs free energy, with an H-theorem for the isothermal unforced system and mass conservation as its zeroth moment. A single dimensionless group, the pore-resolved Damkohler number Da(r,x), organizes the behavior and unifies phenomenologies long modelled separately. A Chapman-Enskog reduction identifies Richards' equation as the quasi-static (Da->0) limit, with matric potential and hydraulic conductivity K emerging only there and K vanishing below the percolation threshold; capillary-bundle and critical-path models are its diagonal and spectral limits. Hysteresis is the holonomy of a forcing bundle, a geometric phase rather than per-pore bistability, with a falsifiable loop-area law H ~ I^2. Preferential flow is what the same equation does where Da>1, so the Richards/preferential-flow dichotomy becomes a continuous Da-controlled crossover. Out of the quasi-static limit g(r) is the irreducible state variable. All inputs are geometric properties of the pore network, measurable from micro-CT and calibrated against no macroscopic data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.09416",
  "author_total": 1,
  "authors": [
    {
      "name": "Riccardo Rigon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqdr5y7txjdge.bib",
  "cited_by": 1,
  "doi": "10.48550/arxiv.2607.09416",
  "fulltext_url": null,
  "id": "fqdr5y7txjdge",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09416",
  "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"
    ],
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "2205|Soil and Unsaturated Flow"
    ]
  ],
  "openalex": "W7168173092",
  "pdf_url": "https://arxiv.org/pdf/2607.09416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqdr5y7txjdge.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2607.09416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09416"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Statistical physics of unsaturated soil water: kinetic theory and non commutative pore water dynamics",
  "title_text": "The Statistical physics of unsaturated soil water: kinetic theory and non commutative pore water dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:14Z",
  "url": "https://research.draconitic.com/paper/fqdr5y7txjdge",
  "venue": "arXiv",
  "versions": []
}