Some interesting consequences of the maximum entropy production principle
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AL, NONLINEAR, AND SOFT MATTER PHYSICS
Some Interesting Consequences of the Maximum Entropy Production Principle L. M. Martyushev Institute of Industrial Ecology, Ural Division, Russian Academy of Sciences, Yekaterinburg, 620219 Russia e-mail: [email protected] Received September 8, 2006
Abstract—Two nonequilibrium phase transitions (morphological and hydrodynamic) are analyzed by applying the maximum entropy production principle. Quantitative analysis is for the first time compared with experiment. Nonequilibrium crystallization of ice and laminar–turbulent flow transition in a circular pipe are examined as examples of morphological and hydrodynamic transitions, respectively. For the latter transition, a minimum critical Reynolds number of 1200 is predicted. A discussion of this important and interesting result is presented. PACS numbers: 05.70.Ln, 47.27.Cn, 81.10.Aj DOI: 10.1134/S1063776107040152
1. INTRODUCTION In recent years, the maximum entropy production principle (MEPP) has been increasingly applied in physics, chemistry, and biology (see reviews in [1, 2]). However, most of these studies have a pronounced theoretical orientation: the focus is either on the foundation and origins of the principle (e.g., see [3–5]) or on its use in analysis of a particular mathematical model of a natural phenomenon (e.g., see [6–8]). In the latter case, comparison with experiment is most frequently made on a qualitative basis. These lines of research have led to significant accomplishments. At the same time, there are practically no studies involving quantitative comparison of consequences of MEPP with available experiments or, more interestingly, quantitative prediction of important, experimentally verifiable facts. Analysis of examples of this kind is the subject of this study. According to MEPP, a nonequilibrium system subject to perturbations of sufficiently large amplitude selects a state characterized by maximum entropy production rate. Therefore, calculations using MEPP are easiest to validate when the evolution of the system involves a first-order (jumplike) phase transition.1 Then, the pre- and posttransition states can be compared in terms of entropy production. The change in entropy production rate across the transition point must be positive. More precisely, it must be close to zero when the evolving system is subject to relatively high noise levels (in the vicinity of the so-called binodal) and substantial when the noise level is so low that the 1
For a system that does not undergo a nonequilibrium transition, a possibility of indirect validation of MEPP using experimental data was demonstrated in our earlier work [9]. However, that study was qualitative.
pretransition state reached by the system is well inside the metastable region. However, while nonequilibrium transitions of this kind are numerous, the accuracy of experimental data found in the literature is seldom sufficient for calculating the entropy production rate. The two examples considered in this paper are free of this shortcoming. 2. MORPHOLOGICAL
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