http://www.mdpi.com/journal/entropy/special_issues/entropy-production/ 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 Submission All papers should be submitted to entropy@mdpi.com with copy to the guest editor. To be published continuously until the deadline and papers will be listed together at the special websites. Both, research articles and review articles are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editors for announcment on this website. Submitted papers should not have been published previously, nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors, sample copies and other relevant information for submitting papers are available on the Instructions for Authors page. Entropy is an international peer-reviewed quarterly journal published by MDPI. Please visit the Instructions for Authors page before submitting a paper. Open Access publication fees are 800 CHF per paper. English correction fees (250 CHF) will be added in certain cases (1050 CHF per paper for those papers that require extensive additional formatting and/or English corrections.). http://www.mdpi.com/1099-4300/12/5/996/ 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. http://www.mdpi.com/1099-4300/12/5/996/ Tue, 27 Apr 2010 00:00:00 CEST Entropy 2010-04-27 12 5 Article 996 1005 1099-4300 The Maximum Entropy Production Principle and Linear Irreversible Processes 2010-04-27 doi: 10.3390/e12050996 Županović Kuić Lošić Petrov Juretić Brumen http://www.mdpi.com/1099-4300/12/4/926/ 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. http://www.mdpi.com/1099-4300/12/4/926/ Wed, 14 Apr 2010 00:00:00 CEST Entropy 2010-04-14 12 4 Article 926 931 1099-4300 On the Problem of Formulating Principles in Nonequilibrium Thermodynamics 2010-04-14 doi: 10.3390/e12040926 Županović Kuić Juretić Dobovišek http://www.mdpi.com/1099-4300/12/3/613/ 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. http://www.mdpi.com/1099-4300/12/3/613/ Mon, 22 Mar 2010 00:00:00 CET Entropy 2010-03-22 12 3 Article 613 630 1099-4300 The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System 2010-03-22 doi: 10.3390/e12030613 Dyke Kleidon http://www.mdpi.com/1099-4300/12/3/473/ 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. http://www.mdpi.com/1099-4300/12/3/473/ Thu, 11 Mar 2010 00:00:00 CET Entropy 2010-03-11 12 3 Article 473 479 1099-4300 Relaxation Processes and the Maximum Entropy Production Principle 2010-03-11 doi: 10.3390/e12030473 Paško Županović Srećko Botrić Davor Juretić Domagoj Kuić http://www.mdpi.com/1099-4300/12/1/107/ 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. http://www.mdpi.com/1099-4300/12/1/107/ Mon, 18 Jan 2010 00:00:00 CET Entropy 2010-01-18 12 1 Article 107 126 1099-4300 From Maximum Entropy to Maximum Entropy Production: A New Approach 2010-01-18 doi: 10.3390/e12010107 Nathaniel Virgo http://www.mdpi.com/1099-4300/11/4/1042/ 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). http://www.mdpi.com/1099-4300/11/4/1042/ Tue, 08 Dec 2009 00:00:00 CET Entropy 2009-12-08 11 4 Article 1042 1054 1099-4300 Modeling Electric Discharges with Entropy Production Rate Principles 2009-12-08 doi: 10.3390/e11041042 Thomas Christen http://www.mdpi.com/1099-4300/11/4/945/ 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. http://www.mdpi.com/1099-4300/11/4/945/ Mon, 30 Nov 2009 00:00:00 CET Entropy 2009-11-30 11 4 Article 945 948 1099-4300 A Story and a Recommendation about the Principle of Maximum Entropy Production 2009-11-30 doi: 10.3390/e11040945 Garth W. Paltridge http://www.mdpi.com/1099-4300/11/4/931/ 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. http://www.mdpi.com/1099-4300/11/4/931/ Fri, 27 Nov 2009 00:00:00 CET Entropy 2009-11-27 11 4 Article 931 944 1099-4300 Maximum Entropy Production as an Inference Algorithm that Translates Physical Assumptions into Macroscopic Predictions: Don’t Shoot the Messenger 2009-11-27 doi: 10.3390/e11040931 Roderick C. Dewar