E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Special Issue "What Is Maximum Entropy Production and How Should We Apply It?"

Quicklinks

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

Deadline for manuscript submissions: closed (31 October 2009)

Special Issue Editors

Guest Editor
Dr. Axel Kleidon (Website)

Max-Planck-Institut fuer Biogeochemie, Postfach 10 01 64, 07701 Jena, Germany
Fax: +49 3641 57 7217
Interests: biodiversity; maximum entropy production; thermodynamics and optimality in the Earth system; Gaia hypothesis; global dynamic vegetation models
Guest Editor
Dr. James Dyke

Max Planck Institut für Biogeochemie, Hans Knöll Str. 10, 07745 Jena, Germany

Special Issue Information

Dear Colleagues,

The proposed principle of Maximum Entropy Production (MEP) states that the steady state of open thermodynamic systems with sufficient degrees of freedom are maintained in a state at which the production of entropy is maximized given the constraints of the system. Similar/related principles have a long history, e.g. the maximum power principle (e.g. applied to biological systems by Lotka in 1922). Recently, it has gained increased attention, and theoretical progress has been made as reflected by a series of papers by Dewar on an information theoretical derivation of this principle. This raises questions about how this principle should be interpreted and applied. This special section would focus on different interpretations by some of the leading researchers in this field.

Format:

- scope: to provide a set of essays to illustrate the different views on the justification and application of the proposed principle of Maximum Entropy Production (MEP).

- motivation: the motivation for the issue comes out of a discussion at a recent workshop held in May 2009 at the Max-Planck-Institut für Biogeochemie in Jena, Germany, on the topic of “Maximum Entropy Production in the Earth System”. This discusion illustrated needs for clarification and interpretation of the different view angles of MEP (MaxEnt interpretation vs. thermodynamic application). The invited and contributed essays of this special section would help to clarify this important theoretical foundation.

James Dyke, Ph. D.
Axel Kleidon, Ph. D.
Guest Editors

Published Papers (8 papers)

View options order results:
result details:
Displaying articles 1-8
Export citation of selected articles as:

Research

Open AccessArticle The Maximum Entropy Production Principle and Linear Irreversible Processes
Entropy 2010, 12(5), 996-1005; doi:10.3390/e12050996
Received: 13 March 2010 / Accepted: 23 April 2010 / Published: 27 April 2010
Cited by 10 | PDF Full-text (107 KB) | HTML Full-text | XML Full-text
Abstract
It is shown that Onsager’s principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of [...] Read more.
It is shown that Onsager’s principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of stationary processes, that this extremum is a maximum rather than a minimum. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle On the Problem of Formulating Principles in Nonequilibrium Thermodynamics
Entropy 2010, 12(4), 926-931; doi:10.3390/e12040926
Received: 24 March 2010 / Accepted: 8 April 2010 / Published: 14 April 2010
Cited by 4 | PDF Full-text (73 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, [...] Read more.
In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, relaxation processes rather than stationary processes are more appropriate for the formulation of principles in nonequilibrium thermodynamics. Arguing that slow varying relaxation can be described with quasi-stationary process, it is shown for two special cases, linear nonequilibrium thermodynamics and linearized Boltzmann equation, that solutions of these problems are in accordance with the maximum entropy production principle. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System
Entropy 2010, 12(3), 613-630; doi:10.3390/e12030613
Received: 24 December 2009 / Revised: 11 March 2010 / Accepted: 19 March 2010 / Published: 22 March 2010
Cited by 20 | PDF Full-text (1221 KB)
Abstract
The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all [...] Read more.
The Maximum Entropy Production (MEP) principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle Relaxation Processes and the Maximum Entropy Production Principle
Entropy 2010, 12(3), 473-479; doi:10.3390/e12030473
Received: 19 February 2010 / Accepted: 9 March 2010 / Published: 11 March 2010
Cited by 1 | PDF Full-text (93 KB) | HTML Full-text | XML Full-text
Abstract
Spontaneous transitions of an isolated system from one macroscopic state to another (relaxation processes) are accompanied by a change of entropy. Following Jaynes’ MaxEnt formalism, it is shown that practically all the possible microscopic developments of a system, within a fixed time [...] Read more.
Spontaneous transitions of an isolated system from one macroscopic state to another (relaxation processes) are accompanied by a change of entropy. Following Jaynes’ MaxEnt formalism, it is shown that practically all the possible microscopic developments of a system, within a fixed time interval, are accompanied by the maximum possible entropy change. In other words relaxation processes are accompanied by maximum entropy production. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle From Maximum Entropy to Maximum Entropy Production: A New Approach
Entropy 2010, 12(1), 107-126; doi:10.3390/e12010107
Received: 30 November 2009 / Revised: 12 January 2010 / Accepted: 14 January 2010 / Published: 18 January 2010
Cited by 10 | PDF Full-text (380 KB) | HTML Full-text | XML Full-text
Abstract
Evidence from climate science suggests that a principle of maximum thermodynamic entropy production can be used to make predictions about some physical systems. I discuss the general form of this principle and an inherent problem with it, currently unsolved by theoretical approaches: [...] Read more.
Evidence from climate science suggests that a principle of maximum thermodynamic entropy production can be used to make predictions about some physical systems. I discuss the general form of this principle and an inherent problem with it, currently unsolved by theoretical approaches: how to determine which system it should be applied to. I suggest a new way to derive the principle from statistical mechanics, and present a tentative solution to the system boundary problem. I discuss the need for experimental validation of the principle, and its impact on the way we see the relationship between thermodynamics and kinetics. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Figures

Open AccessArticle Modeling Electric Discharges with Entropy Production Rate Principles
Entropy 2009, 11(4), 1042-1054; doi:10.3390/e11041042
Received: 29 October 2009 / Accepted: 1 December 2009 / Published: 8 December 2009
Cited by 11 | PDF Full-text (210 KB) | HTML Full-text | XML Full-text
Abstract
Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas) discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production [...] Read more.
Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas) discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP). Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear) physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s). Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle A Story and a Recommendation about the Principle of Maximum Entropy Production
Entropy 2009, 11(4), 945-948; doi:10.3390/e11040945
Received: 23 October 2009 / Accepted: 26 November 2009 / Published: 30 November 2009
Cited by 6 | PDF Full-text (70 KB) | HTML Full-text | XML Full-text
Abstract
The principle of maximum entropy production (MEP) is the subject of considerable academic study, but has yet to become remarkable for its practical applications. A tale is told of an instance in which a spin-off from consideration of an MEP-constrained climate model [...] Read more.
The principle of maximum entropy production (MEP) is the subject of considerable academic study, but has yet to become remarkable for its practical applications. A tale is told of an instance in which a spin-off from consideration of an MEP-constrained climate model at least led to re-consideration of the very practical issue of water-vapour feedback in climate change. Further, and on a more-or-less unrelated matter, a recommendation is made for further research on whether there might exist a general "rule" whereby, for certain classes of complex non-linear systems, a state of maximum entropy production is equivalent to a state of minimum entropy. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)
Open AccessArticle Maximum Entropy Production as an Inference Algorithm that Translates Physical Assumptions into Macroscopic Predictions: Don’t Shoot the Messenger
Entropy 2009, 11(4), 931-944; doi:10.3390/e11040931
Received: 23 October 2009 / Accepted: 23 November 2009 / Published: 27 November 2009
Cited by 39 | PDF Full-text (268 KB) | HTML Full-text | XML Full-text
Abstract
Is Maximum Entropy Production (MEP) a physical principle? In this paper I tentatively suggest it is not, on the basis that MEP is equivalent to Jaynes’ Maximum Entropy (MaxEnt) inference algorithm that passively translates physical assumptions into macroscopic predictions, as applied to [...] Read more.
Is Maximum Entropy Production (MEP) a physical principle? In this paper I tentatively suggest it is not, on the basis that MEP is equivalent to Jaynes’ Maximum Entropy (MaxEnt) inference algorithm that passively translates physical assumptions into macroscopic predictions, as applied to non-equilibrium systems. MaxEnt itself has no physical content; disagreement between MaxEnt predictions and experiment falsifies the physical assumptions, not MaxEnt. While it remains to be shown rigorously that MEP is indeed equivalent to MaxEnt for systems arbitrarily far from equilibrium, work in progress tentatively supports this conclusion. In terms of its role within non-equilibrium statistical mechanics, MEP might then be better understood as Messenger of Essential Physics. Full article
(This article belongs to the Special Issue What Is Maximum Entropy Production and How Should We Apply It?)

Journal Contact

MDPI AG
Entropy Editorial Office
St. Alban-Anlage 66, 4052 Basel, Switzerland
entropy@mdpi.com
Tel. +41 61 683 77 34
Fax: +41 61 302 89 18
Editorial Board
Contact Details Submit to Entropy
Back to Top