Special Issue "Maximum Entropy Production"


A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 October 2013)

Special Issue Editor

Guest Editor
Dr. Robert Niven
School of Engineering and Information Technology, The University of New South Wales at ADFA, Northcott Drive, Canberra, ACT, 2600, Australia
Website: http://seit.unsw.adfa.edu.au/research/staff_detail.php?staff_id=1078
Interests: combinatorial basis of entropy (Boltzmann principle); maximum entropy analysis of scientific, engineering and human systems; equilibrium and non-equilibrium thermodynamics; entropy extremum methods; turbulent fluid mechanics

Special Issue Information

Dear Colleagues,

There is at present a strong and growing interest in extremum principles based on the thermodynamic entropy production (and allied concepts), for the analysis of non-equilibrium (flow) systems of all types. This perspective was initiated by seminal contributions by Helmholtz, Rayleigh, Jaumann and many others in the 19th and early 20th centuries, and significantly advanced by the linear theory of Onsager during the 1930s to 1950s, with its accompanying Curie postulate. A minimum entropy production (MinEP) principle, for the selection of the stationary (steady state) flow from a set of non-steady flows, was developed by Prigogine in the 1960s. A maximum entropy production (MaxEP) principle or hypothesis was developed empirically by Paltridge and later workers from the 1970s, for the construction of planetary heat transfer models. While seemingly opposite to Prigogine's concept, this MaxEP hypothesis has a different purpose: it seeks to select the observable steady state from a set of physically possible but unrealised steady states. A separate, allied framework of maximum dissipation or MaxEP methods was also developed by Zeigler from the 1970s, mainly for the analysis of solid and thermodynamic continua. More recently, a wide range of additional MinEP, MaxEP and allied variational principles and/or empiricisms have been proposed, and in some cases derived on theoretical grounds. Many of the theoretical studies invoke the maximum entropy (MaxEnt) method developed by Jaynes, as the starting point or primary tool of their analysis.

MaxEP methods have now been invoked or applied to the analysis of an extraordinarily broad assortment of non-equilibrium phenomena. These include: convective heat transfer systems (including Benard cells and planetary atmospheric, mantle and core convective phenomena); coupled planetary biogeochemical and geological processes and the development of planetary ecosystems (with connections to origins and evolution of life); the development of local biochemical processes and ecosystems over molecular to regional scales (including prediction of their properties); crystal nucleation, growth and the development of mineral assemblages in chemical and geological systems; engineering mechanics, plastic deformation and fracture mechanics in solid continua (with application to earthquake frequency prediction and modelling); viscous, turbulent and electromagnetic dissipation and the phenomenon of turbulence in liquids, gases and plasmas; the analysis and optimisation of flow networks of all types (including of electrical, fluid, traffic, communications signal and other quantities, and of chemical reaction systems); and the analysis and prediction of human transport, communication, industrial, economic, technological, political and social systems.

As demonstrated by several recent contributions to the published literature and earnest discussions in major conferences, there is still considerable controversy over both the theoretical foundations and application of entropy production extremum principles. Many of the definitions and purpose of such concepts - for example, whether they are applicable only to stationary states or can be extended to transient phenomena, or whether they concern closed or open systems - remain in confusion. Many highly respected researchers throughout the sciences and engineering remain sceptical of the very existence, or at least the methodological toolkit, precision or technical rigour of application of such methods. For this special issue, we therefore seek additional, defensible, technically rigorous contributions to this field, spanning all possible theoretical approaches, as well as the application of such methods to all possible observable systems. In so doing, we seek to resolve some of the controversies in this very broad field, and to clarify the content and purpose of the "working knowledge" of this field.

We therefore welcome your contributions to this special issue.

Dr. Robert K. Niven
Guest Editor


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. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as 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 refereed through a 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 1400 CHF (Swiss Francs).


  • entropy production
  • maximum entropy production
  • minimum entropy production
  • variational
  • extremum
  • inference
  • maximum entropy
  • maximum relative entropy
  • non-equilibrium thermodynamics
  • dissipative structure
  • thermodynamic force
  • thermodynamic gradient
  • degradation
  • dissipation
  • chemical reaction network
  • fluid mechanics

Published Papers (8 papers)

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Displaying article 1-8
p. 2291-2308
Entropy 2014, 16(4), 2291-2308; doi:10.3390/e16042291
Received: 5 January 2014 / Revised: 10 March 2014 / Accepted: 14 April 2014 / Published: 22 April 2014
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(This article belongs to the Special Issue Maximum Entropy Production)
p. 1037-1046
by , ,  and
Entropy 2014, 16(2), 1037-1046; doi:10.3390/e16021037
Received: 25 November 2013 / Revised: 6 January 2014 / Accepted: 10 February 2014 / Published: 19 February 2014
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(This article belongs to the Special Issue Maximum Entropy Production)
p. 5053-5064
by , ,  and
Entropy 2013, 15(11), 5053-5064; doi:10.3390/e15115053
Received: 13 September 2013 / Revised: 25 October 2013 / Accepted: 15 November 2013 / Published: 19 November 2013
Show/Hide Abstract | Cited by 2 | PDF Full-text (251 KB)
(This article belongs to the Special Issue Maximum Entropy Production)
p. 2846-2860
by  and
Entropy 2013, 15(7), 2846-2860; doi:10.3390/e15072846
Received: 26 April 2013 / Revised: 5 July 2013 / Accepted: 17 July 2013 / Published: 19 July 2013
Show/Hide Abstract | Cited by 1 | PDF Full-text (728 KB)
(This article belongs to the Special Issue Maximum Entropy Production)
p. 2570-2584
Entropy 2013, 15(7), 2570-2584; doi:10.3390/e15072570
Received: 14 March 2013 / Revised: 20 May 2013 / Accepted: 21 June 2013 / Published: 28 June 2013
Show/Hide Abstract | Cited by 4 | PDF Full-text (269 KB)
(This article belongs to the Special Issue Maximum Entropy Production)
p. 1503-1515
by , ,  and
Entropy 2013, 15(5), 1503-1515; doi:10.3390/e15051503
Received: 4 March 2013 / Revised: 17 April 2013 / Accepted: 19 April 2013 / Published: 25 April 2013
Show/Hide Abstract | Cited by 5 | PDF Full-text (320 KB)
(This article belongs to the Special Issue Maximum Entropy Production)
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p. 1152-1170
Entropy 2013, 15(4), 1152-1170; doi:10.3390/e15041152
Received: 17 January 2013 / Revised: 11 March 2013 / Accepted: 18 March 2013 / Published: 26 March 2013
Show/Hide Abstract | Cited by 11 | PDF Full-text (325 KB)
(This article belongs to the Special Issue Maximum Entropy Production)
p. 2478-2491
by ,  and
Entropy 2012, 14(12), 2478-2491; doi:10.3390/e14122478
Received: 25 September 2012 / Revised: 19 October 2012 / Accepted: 30 November 2012 / Published: 4 December 2012
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Last update: 13 May 2013

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