{
  "annotation_id": "1f8b2d2f-3201-4a95-b982-79541c0a4d36",
  "date_created": "2026-03-02T18:01:35.713000Z",
  "date_modified": "2026-03-02T18:01:35.713000Z",
  "file_hash": "3da24785a9e056f2ad173597dc6be256d1e417e9a7b5d89c26e8a3e79214a87a",
  "private": false,
  "record": {
    "abstract": "All living cells transport molecules and ions across membranes, often against\nconcentration gradients. This active transport requires continual energy\nexpenditure and is clearly a nonequilibrium process for which standard\nequilibrium thermodynamics is not rigorously applicable. Here we derive a\nnonequilibrium effective potential that evaluates the per particle transport\nenergy invested by the membrane. A novel method is used whereby a Hamiltonian\nfunction is constructed using particle concentrations as generalized\ncoordinates. The associated generalized momenta are simply related to the\nindividual particle energy from which we identify the effective potential.\nExamples are given and the formalism is compared with the equilibrium Gibb\u0027s\nfree energy.",
    "arxiv_id": "q-bio/0702026",
    "authors": [
      "Robert W. Finkel"
    ],
    "categories": [
      "q-bio.SC",
      "q-bio.QM"
    ],
    "title": "Effective Potential Energy Expression for Membrane Transport",
    "url": "https://arxiv.org/abs/q-bio/0702026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "75626870-e8a3-4bcb-abaa-b19594b51708",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}