{
  "id": "1108.4055",
  "version": "v2",
  "published": "2011-08-19T21:48:45.000Z",
  "updated": "2011-08-31T11:42:32.000Z",
  "title": "Thermodynamics and Geometry of Reversible and Irreversible Markov Processes",
  "authors": [
    "Hao Ge",
    "Woo H. Kim",
    "Hong Qian"
  ],
  "comment": "4 pages; no figure This paper has been withdrawn by the authors due to a crucial error in the master-equation part",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Master equation with microscopic reversibility ($q_{ij}\\neq 0$ iff $q_{ji}\\neq 0$) has a {\\em thermodynamic superstructure} in terms of two state functions $S$, entropy, and $F$, free energy: It is discovered recently that entropy production rate $e_p=-dF/dt+Q_{hk}$ with both $-dF/dt=f_d, Q_{hk} \\ge 0$. The free energy dissipation $f_d\\ge 0$ reflects irreversibility in spontaneous self-organization; house-keeping heat $Q_{hk}\\ge 0$ reveals broken time-symmetry in open system driven away from equilibrium. In a Riemannian geometric space, the master equation is a geodesic flow when $Q_{hk}=0$; here we show that the $e_p$ decomposition is orthogonal: $e_p$, $f_d$, $Q_{hk}$ forms a pythagorean triples. Gradient flow means {\\em maximum dissipation principle} outside Onsager's regime. The presence of $Q_{hk}$ makses gradient flow no longer generally true. Thermodynamics of stochastic physics requires a new geometric perspective.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-31T11:42:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "irreversible markov processes",
      "thermodynamic",
      "master equation",
      "open system driven away",
      "entropy production rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4055G"
    }
  }
}