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Maximum Entropy Production
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Maximum Entropy Production

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

Deadline for manuscript submissions: closed (30 October 2013) | Viewed by 59393

Special Issue Editor

Dr. Robert Niven

E-Mail Website
Guest Editor
School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, Australia
Interests: Bayesian and maximum entropy methods for the analysis of engineering and scientific systems; theoretical foundations of Bayesian inference; Bayesian estimation and plausible reasoning; entropy-based inference and extremum methods; Bayesian risk assessment; heuristics and methods for the selection of prior probabilities; probabilistic transport and evolution equations and operators
Special Issues, Collections and Topics in MDPI journals

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

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Keywords

  • 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

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Published Papers (8 papers)

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Research

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342 KiB  
Article
On the Clausius-Duhem Inequality and Maximum Entropy Production in a Simple Radiating System
by Joachim Pelkowski
Entropy 2014, 16(4), 2291-2308; https://doi.org/10.3390/e16042291 - 22 Apr 2014
Cited by 11 | Viewed by 7936
Abstract
A black planet irradiated by a sun serves as the archetype for a simple radiating two-layer system admitting of a continuum of steady states under steadfast insolation. Steady entropy production rates may be calculated for different opacities of one of the layers, explicitly [...] Read more.
A black planet irradiated by a sun serves as the archetype for a simple radiating two-layer system admitting of a continuum of steady states under steadfast insolation. Steady entropy production rates may be calculated for different opacities of one of the layers, explicitly so for the radiative interactions, and indirectly for all the material irreversibilities involved in maintaining thermal uniformity in each layer. The second law of thermodynamics is laid down in two versions, one of which is the well-known Clausius-Duhem inequality, the other being a modern version known as the entropy inequality. By maximizing the material entropy production rate, a state may be selected that always fulfills the Clausius-Duhem inequality. Some formally possible steady states, while violating the latter, still obey the entropy inequality. In terms of Earth’s climate, global entropy production rates exhibit extrema for any “greenhouse effect”. However, and only insofar as the model be accepted as representative of Earth’s climate, the extrema will not be found to agree with observed (effective) temperatures assignable to both the atmosphere and surface. This notwithstanding, the overall entropy production for the present greenhouse effect on Earth is very close to the maximum entropy production rate of a uniformly warm steady state at the planet’s effective temperature. For an Earth with a weak(er) greenhouse effect the statement is no longer true. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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323 KiB  
Article
Maximum Entropy Production vs. Kolmogorov-Sinai Entropy in a Constrained ASEP Model
by Martin Mihelich, Bérengère Dubrulle, Didier Paillard and Corentin Herbert
Entropy 2014, 16(2), 1037-1046; https://doi.org/10.3390/e16021037 - 19 Feb 2014
Cited by 10 | Viewed by 6710
Abstract
The asymmetric simple exclusion process (ASEP) has become a paradigmatic toy-model of a non-equilibrium system, and much effort has been made in the past decades to compute exactly its statistics for given dynamical rules. Here, a different approach is developed; analogously to the [...] Read more.
The asymmetric simple exclusion process (ASEP) has become a paradigmatic toy-model of a non-equilibrium system, and much effort has been made in the past decades to compute exactly its statistics for given dynamical rules. Here, a different approach is developed; analogously to the equilibrium situation, we consider that the dynamical rules are not exactly known. Allowing for the transition rate to vary, we show that the dynamical rules that maximize the entropy production and those that maximise the rate of variation of the dynamical entropy, known as the Kolmogorov-Sinai entropy coincide with good accuracy. We study the dependence of this agreement on the size of the system and the couplings with the reservoirs, for the original ASEP and a variant with Langmuir kinetics. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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251 KiB  
Article
Multiscale Mesoscopic Entropy of Driven Macroscopic Systems
by Miroslav Grmela, Giuseppe Grazzini, Umberto Lucia and L'Hocine Yahia
Entropy 2013, 15(11), 5053-5064; https://doi.org/10.3390/e15115053 - 19 Nov 2013
Cited by 13 | Viewed by 5013
Abstract
How do macroscopic systems react to imposed external forces? Attempts to answer this question by a general principle have a long history. The general feeling is that the macroscopic systems in their reaction to imposed external forces follow some kind of optimization strategy [...] Read more.
How do macroscopic systems react to imposed external forces? Attempts to answer this question by a general principle have a long history. The general feeling is that the macroscopic systems in their reaction to imposed external forces follow some kind of optimization strategy in which their internal structure is changed so that they offer the least possible resistance. What is the potential involved in such optimization? It is often suggested that it is entropy or entropy production. But entropy is a potential arising in thermodynamics of externally unforced macroscopic systems. What exactly shall we understand by a mesoscopic entropy of externally driven systems and how shall we find it for a specific macroscopic system? Full article
(This article belongs to the Special Issue Maximum Entropy Production)
728 KiB  
Article
Maximum Entropy Production and Time Varying Problems: The Seasonal Cycle in a Conceptual Climate Model
by Didier Paillard and Corentin Herbert
Entropy 2013, 15(7), 2846-2860; https://doi.org/10.3390/e15072846 - 19 Jul 2013
Cited by 7 | Viewed by 6563
Abstract
It has been suggested that the maximum entropy production (MEP) principle, or MEP hypothesis, could be an interesting tool to compute climatic variables like temperature. In this climatological context, a major limitation of MEP is that it is generally assumed to be applicable [...] Read more.
It has been suggested that the maximum entropy production (MEP) principle, or MEP hypothesis, could be an interesting tool to compute climatic variables like temperature. In this climatological context, a major limitation of MEP is that it is generally assumed to be applicable only for stationary systems. It is therefore often anticipated that critical climatic features like the seasonal cycle or climatic change cannot be represented within this framework. We discuss here several possibilities in order to introduce time- varying climatic problems using the MEP formalism. We will show that it is possible to formulate a MEP model which accounts for time evolution in a consistent way. This formulation leads to physically relevant results as long as the internal time scales associated with thermal inertia are small compared to the speed of external changes. We will focus on transient changes as well as on the seasonal cycle in a conceptual climate box-model in order to discuss the physical relevance of such an extension of the MEP framework. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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269 KiB  
Article
Fact-Checking Ziegler’s Maximum Entropy Production Principle beyond the Linear Regime and towards Steady States
by Matteo Polettini
Entropy 2013, 15(7), 2570-2584; https://doi.org/10.3390/e15072570 - 28 Jun 2013
Cited by 29 | Viewed by 6683
Abstract
We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In [...] Read more.
We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In particular: (1) we show that Ziegler’s principle of thermodynamic orthogonality leads to stringent reciprocal relations for higher order response coefficients, and in the framework of stochastic thermodynamics, we exhibit a simple explicit model that does not satisfy them; (2) on a network, enforcing Kirchhoff’s current law, we show that maximization of the entropy production prescribes reciprocal relations between coarse-grained observables, but is not responsible for the onset of the steady state, which is, rather, due to the minimum entropy production principle. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
320 KiB  
Article
Time Reversibility, Correlation Decay and the Steady State Fluctuation Relation for Dissipation
by Debra J. Searles, Barbara M. Johnston, Denis J. Evans and Lamberto Rondoni
Entropy 2013, 15(5), 1503-1515; https://doi.org/10.3390/e15051503 - 25 Apr 2013
Cited by 13 | Viewed by 6121
Abstract
Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of [...] Read more.
Steady state fluctuation relations for nonequilibrium systems are under intense investigation because of their important practical implications in nanotechnology and biology. However the precise conditions under which they hold need clarification. Using the dissipation function, which is related to the entropy production of linear irreversible thermodynamics, we show time reversibility, ergodic consistency and a recently introduced form of correlation decay, called T-mixing, are sufficient conditions for steady state fluctuation relations to hold. Our results are not restricted to a particular model and show that the steady state fluctuation relation for the dissipation function holds near or far from equilibrium subject to these conditions. The dissipation function thus plays a comparable role in nonequilibrium systems to thermodynamic potentials in equilibrium systems. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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250 KiB  
Article
Maximum Entropy Gibbs Density Modeling for Pattern Classification
by Neila Mezghani, Amar Mitiche and Mohamed Cheriet
Entropy 2012, 14(12), 2478-2491; https://doi.org/10.3390/e14122478 - 4 Dec 2012
Cited by 2 | Viewed by 6780
Abstract
Recent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category [...] Read more.
Recent studies have shown that the Gibbs density function is a good model for visual patterns and that its parameters can be learned from pattern category training data by a gradient algorithm optimizing a constrained entropy criterion. These studies represented each pattern category by a single density. However, the patterns in a category can be so complex as to require a representation spread over several densities to more accurately account for the shape of their distribution in the feature space. The purpose of the present study is to investigate a representation of visual pattern category by several Gibbs densities using a Kohonen neural structure. In this Gibbs density based Kohonen network, which we call a Gibbsian Kohonen network, each node stores the parameters of a Gibbs density. Collectively, these Gibbs densities represent the pattern category. The parameters are learned by a gradient update rule so that the corresponding Gibbs densities maximize entropy subject to reproducing observed feature statistics of the training patterns. We verified the validity of the method and the efficiency of the ensuing Gibbs density pattern representation on a handwritten character recognition application. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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Review

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325 KiB  
Review
Entropy and Entropy Production: Old Misconceptions and New Breakthroughs
by Leonid M. Martyushev
Entropy 2013, 15(4), 1152-1170; https://doi.org/10.3390/e15041152 - 26 Mar 2013
Cited by 135 | Viewed by 12264
Abstract
Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings). The first misunderstanding: entropy is a [...] Read more.
Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings). The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress) in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it. Full article
(This article belongs to the Special Issue Maximum Entropy Production)
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