{
  "id": "cond-mat/0604414",
  "version": "v2",
  "published": "2006-04-18T11:54:39.000Z",
  "updated": "2007-08-13T14:53:55.000Z",
  "title": "Kinetic theory with angle-action variables",
  "authors": [
    "Pierre-Henri Chavanis"
  ],
  "journal": "Physica A, 377, 469 (2007)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the distribution function of the system as a whole due to resonances between different orbits. This equation is written in angle-action variables. It conserves mass and energy and increases the Boltzmann entropy (H-theorem). Using a thermal bath approximation, we derive a Fokker-Planck equation that describes the relaxation of a test particle towards the Boltzmann distribution under the combined effect of diffusion and friction terms. We mention some analogies with the kinetic theory of point vortices in two-dimensional hydrodynamics. We also stress the limitations of our approach and the connection with recent works.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-13T14:53:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kinetic theory",
      "angle-action variables",
      "weak long-range interactions",
      "thermal bath approximation",
      "quasilinear theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}