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PreprintCC BY 4.0arXiv

Derivation of Fokker-Planck equation and its entropy production

  • Tânia Tomé
  • Mário J. de Oliveira
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Abstract

We derive the Fokker-Planck equation and its entropy production from the master equation. To this end we consider a discrete space of states where the master equation is defined and appropriate transition rates are introduced. A transition rate has two parts, one of which is the ordinary term proportional to the inverse of the spacing and the other is inversely proportional to the square of the spacing corresponding to the variance of the independent stochastic variable. In the continuous space limit, we obtain the Fokker-Planck as well as the rate of entropy production and the flux of entropy. We also consider the case where the space of states is the phase space and discuss the equations appropriate for systems in contact with several heat reservoirs and for isolated systems.

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Cite

BibTeXRIS
BibTeX
@misc{tome2026derivation,
  title = {{Derivation of Fokker-Planck equation and its entropy production}},
  author = {Tânia Tomé and Mário J. de Oliveira},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.36260},
  eprint = {2609.36260},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36260},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Derivation of Fokker-Planck equation and its entropy production
AU  - Tânia Tomé
AU  - Mário J. de Oliveira
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.36260
UR  - https://arxiv.org/abs/2609.36260
AB  - We derive the Fokker-Planck equation and its entropy production from the master equation. To this end we consider a discrete space of states where the master equation is defined and appropriate transition rates are introduced. A transition rate has two parts, one of which is the ordinary term proportional to the inverse of the spacing and the other is inversely proportional to the square of the spacing corresponding to the variance of the independent stochastic variable. In the continuous space limit, we obtain the Fokker-Planck as well as the rate of entropy production and the flux of entropy. We also consider the case where the space of states is the phase space and discuss the equations appropriate for systems in contact with several heat reservoirs and for isolated systems.
ER  -