{
  "id": "1005.1251",
  "version": "v2",
  "published": "2010-05-07T17:00:56.000Z",
  "updated": "2011-02-02T17:02:30.000Z",
  "title": "Thermodynamics of Markov Processes with Non-extensive Entropy and Free Energy",
  "authors": [
    "Hong Qian"
  ],
  "comment": "6 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Parallel to the recent presented complete thermodynamic formalism for master equation systems, we show that a \"thermodynamic\" theory can also be developed based on Tsallis' generalized entropy $S_q and Shiino's generalized free energy F_q which depends on \\pi_i, the stationary distribution of the master equation. $dF_q/dt=-f_d\\le 0$ and it is zero iff the system is in its stationary state. $dS_q/dt = f_d-Q_{ex}$ where $Q_{ex}$ characterizes the heat exchange. For systems approaching equilibrium with detailed balance, $f_d$ is the product of Onsager's thermodynamic flux and force. However, it is discovered that the Onsager's force is non-local. This is a consequence of the particular transformation invariance for zero energy of Tsallis' statistics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-02T17:02:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free energy",
      "markov processes",
      "non-extensive entropy",
      "master equation systems",
      "complete thermodynamic formalism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1251Q"
    }
  }
}