{
  "annotation_id": "01c280f7-0828-4c14-bf00-6b47dc9b632e",
  "date_created": "2026-03-02T18:00:42.877000Z",
  "date_modified": "2026-03-02T18:00:42.877000Z",
  "file_hash": "598fd4f7e90d451343f08216c2c081a335bea94f26d5bc6dfa7e99e63972287c",
  "private": false,
  "record": {
    "abstract": "Fokker-Planck equation with the velocity-dependent coefficients is considered\nfor various isotropic systems on the basis of probability transition (PT)\napproach. This method provides the self-consistent and universal description of\nfriction and diffusion for Brownian particles. Renormalization of the friction\ncoefficient is shown to occur for two dimensional (2-D) and three dimensional\n(3-D) cases, due to the tensorial character of diffusion. The specific forms of\nPT are calculated for the Boltzmann-type of collisions and for the\nabsorption-type of collisions (the later are typical for dusty plasmas and some\nother systems). Validity of the Einstein\u0027s relation for the Boltzmann-type\ncollisions is analyzed for the velocity-dependent friction and diffusion\ncoefficients. For the Boltzmann-type collisions in the region of very high\ngrain velocity as well as it is always for non-Boltzmann collisions, such as,\ne.g., absorption collisions, the Einstein relation is violated, although some\nother relations (determined by the structure of PT) can exist. The generalized\nfriction force is investigated in dusty plasma in the framework of the PT\napproach. The relation between this force, negative collecting friction force\nand scattering and collecting drag forces is established.+AFwAXA- The concept\nof probability transition is used to describe motion of active particles in an\nambient medium. On basis of the physical arguments the PT for a simple model of\nthe active particle is constructed and the coefficients of the relevant\nFokker-Planck equation are found. The stationary solution of this equation is\ntypical for the simplest self-organized molecular machines.+AFwAXA- PACS\nnumber(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-y",
    "arxiv_id": "physics/0212076",
    "authors": [
      "S. A. Trigger"
    ],
    "categories": [
      "physics.plasm-ph"
    ],
    "doi": "10.1103/PhysRevE.67.046403",
    "title": "Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer   probability approach",
    "url": "https://arxiv.org/abs/physics/0212076"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "86f97e3b-20b7-4a0b-9179-2a2eed45ffd2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}