Special Issue "Statistical Mechanics of Nonequilibrium Fluid Flows"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 31 March 2021.

Special Issue Editors

Prof. Dr. Peter W. Egolf
Website1 Website2 Website3
Guest Editor
Institute for Theoretical Turbulence Research, Alte Wildeggerstrasse 5, CH-5702 Niederlenz, Switzerland
Interests: fundamental turbulence research; closure problem; zero-equation turbulence modeling; statistical theories of turbulence; thermodynamics of turbulence; phase transition of turbulence; nonlocal and fractional models of turbulence; turbulent shear flows; Navier–Stokes turbulence
Prof. Dr. Kolumban Hutter
Website1 Website2
Guest Editor
Laboratory of Hydraulics, Hydrology and Glaciology, Hönggerbergring 26, HIA 58D, ETH, CH-8092 Zurich, Switzerland
Interests: continuum field theories; continum methods of physical modeling; foundations of fluid and thermodynamics; hydraulics; hydrology; glaciology; dynamics of glaciers; avalanching flows; mechanics of granular materials; physical limnology; physics of lakes

Special Issue Information

Dear Colleagues,

In turbulence research, in the last few decades, some of the remaining burning questions have been answered, leading to deeper insights into the nature of turbulence. This started, on the one hand, when nonlinear dynamic concepts, e.g., in­sta­bi­li­ties, bifurcation scenarios, self-similartity, fractal geometry, were intro­duced to describe turbulent processes. It became evi­dent that fractal Lévy flight distributions describe intermittency and spatial clustering, both re­lating to a two-phase picture of turbulence with laminar streaks and turbulent patches characterizing the two phases of a possibly dynamical phase transition. On the other hand, equilibrium Boltz­mann–Gibbs thermo­dy­na­mics was generalized to nonequilibrium thermodynamics, today better known by the scientific term nonextensive thermo­dynamics. At present, this domain finds its mathematics in fractional calculus. In 2019, Egolf and Hutter proved that some of the descriptions of fractional derivatives and recently proposed nonlocal descriptions of the Reynolds shear stresses coincide. For a long time, it has been known that turbulence is not only a nonlinear phenomenon, but also one showing nonlocality. Fractional Langevin and Fokker–Planck equations support the deve­lop­ment of such new promising concepts of turbulence. Finally, Alemany and Zanette proved that for the low-wave number regime of turbulent eddies, the probability distribution of Lévy flights directly copes with the nonextensive ther­mo­dy­namics of Tsallis. Through this all the above described theories and models:

  • Nonlinear and nonlocal modeling;
  • Fractal geometry;
  • Fractional calculus;
  • Lévy flight statistics;
  • Nonextensive thermodynamics;

have been proven to be tightly linked. Therefore, it is, for example, impossible to deny the fractal nature or the applicability of Lévy flight statistics to model turbulence without denying the nonlocality and fractionality of turbulence and vice versa. Lévy flight statistics leads to turbulent energy intensity spectra of power law nature describing intermittency, including as a special case the Kolmogorov–Oboukov spectrum.

The present Special Issue of Entropy, “Statistical Mechanics of Nonequilibrium Fluid Flows”, con­tains articles contributing to the modern aspects of turbulence described above. This also contains con­tributions to turbulent flow stability, anomalous diffusion, information theory and turbulence, ge­neralized entropies, e.g., Shan­non entropy, Kolmogorov entropy, Tsallis entropy, non­equi­li­brium and nonextensive thermo­dynamics, phase change models of turbulence, etc.

Prof. Dr. Peter W. Egolf
Prof. Dr. Kolumban Hutter
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Lévy statistics
  • super diffusion
  • hereditary and memory effects
  • nonlocality
  • Lyapunov exponent
  • loss of information
  • Shannon’s entropy
  • generalized entropy
  • nonextensive thermodynamics
  • fractional dynamics
  • fractional Langevin equation
  • fractional Fokker–Planck equation
  • Szilard’s engine
  • Landauer’s principle

Published Papers

This special issue is now open for submission.
Back to TopTop