A Theoretical Basis for Maximum Entropy Production
Maximum entropy production (MaxEP) is a conjectured selection criterion for the stationary states of non-equilibrium systems. In the absence of a firm theoretical basis, MaxEP has largely been applied in an ad hoc manner. Consequently its apparent success
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A Theoretical Basis for Maximum Entropy Production Roderick C. Dewar and Amos Maritan
Abstract Maximum entropy production (MaxEP) is a conjectured selection criterion for the stationary states of non-equilibrium systems. In the absence of a firm theoretical basis, MaxEP has largely been applied in an ad hoc manner. Consequently its apparent successes remain something of a curiosity while the interpretation of its apparent failures is fraught with ambiguity. Here we show how Jaynes’ maximum entropy (MaxEnt) formulation of statistical mechanics provides a theoretical basis for MaxEP which answers two outstanding questions that have so far hampered its wider application: What do the apparent successes and failures of MaxEP actually mean physically? And what is the appropriate entropy production that is maximized in any given problem? As illustrative examples, we show how MaxEnt underpins previous applications of MaxEP to planetary climates and fluid turbulence. We also discuss the relationship of MaxEP to the fluctuation theorem and Ziegler’s maximum dissipation principle.
3.1 MaxEP: What Does It Mean and How Do We Use It? The conjecture of maximum entropy production (MaxEP) as a selection criterion for non-equilibrium stationary states has shown some promising successes in studies of, for example, planetary climates [1, 2], fluid turbulence [3, 4], crystal growth morphology [5, 6], biological evolution and adaptation [7–10], and earthquake dynamics [11]. The practical significance of MaxEP is that it appears to
R. C. Dewar (&) Research School of Biology, The Australian National University, Canberra, ACT 0200, Australia e-mail: [email protected] A. Maritan Department of Physics G. Galilei, University of Padua, Via Marzolo 8, 35131 Padua, Italy
R. C. Dewar et al. (eds.), Beyond the Second Law, Understanding Complex Systems, DOI: 10.1007/978-3-642-40154-1_3, Ó Springer-Verlag Berlin Heidelberg 2014
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R. C. Dewar and A. Maritan
be able to make realistic predictions of non-equilibrium stationary states on the basis of a limited set of dynamical constraints, without having to solve the underlying equations of motion in their full complexity. Potentially MaxEP is a non-equilibrium selection criterion of some generality [12]. However, without a theoretical basis to underpin MaxEP, its wider application has been hampered by two unresolved questions, one conceptual, the other practical: What is the physical interpretation of the apparent successes of MaxEP? And what is the entropy production (EP) function to be maximized in any given problem? In the absence of answers to these two questions, to date MaxEP has been applied in a largely ad hoc manner and its successes remain something of an unexplained curiosity. For example, the early successes of MaxEP using 1-D zonally-averaged energy balance models of Earth’s climate [1, 2] were obtained by maximizing the material EP associated with meridional heat transport in the atmosphere and oceans, even though radiative EP is numerically by far the dominant contrib
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