Fluctuation theorem and extended thermodynamics of turbulence: Fluctuation-theorem and turbulence

Amilcare Porporato, Milad Hooshyar, Andrew D. Bragg, Gabriel Katul

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

Original languageEnglish (US)
Article number0468
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2243
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


  • cascade
  • fluctuation theorem
  • turbulence


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