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Title: Use and validity of principles of extremum of entropy production in the study of complex systems

Abstract

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented. -- Highlights: •The principles of extremum of entropy production are not first principles. •They result from the maximization of conductivities under appropriate constraints. •The conditions of their validity are set explicitly. •Some long-standing controversies are discussed and clarified.

Authors:
Publication Date:
OSTI Identifier:
22314829
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 346; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; LIMITING VALUES; MATHEMATICAL SOLUTIONS; THERMAL CONDUCTIVITY; THERMAL EQUILIBRIUM

Citation Formats

Heitor Reis, A., E-mail: ahr@uevora.pt. Use and validity of principles of extremum of entropy production in the study of complex systems. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.03.013.
Heitor Reis, A., E-mail: ahr@uevora.pt. Use and validity of principles of extremum of entropy production in the study of complex systems. United States. doi:10.1016/J.AOP.2014.03.013.
Heitor Reis, A., E-mail: ahr@uevora.pt. Tue . "Use and validity of principles of extremum of entropy production in the study of complex systems". United States. doi:10.1016/J.AOP.2014.03.013.
@article{osti_22314829,
title = {Use and validity of principles of extremum of entropy production in the study of complex systems},
author = {Heitor Reis, A., E-mail: ahr@uevora.pt},
abstractNote = {It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented. -- Highlights: •The principles of extremum of entropy production are not first principles. •They result from the maximization of conductivities under appropriate constraints. •The conditions of their validity are set explicitly. •Some long-standing controversies are discussed and clarified.},
doi = {10.1016/J.AOP.2014.03.013},
journal = {Annals of Physics (New York)},
number = Complete,
volume = 346,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 2014},
month = {Tue Jul 15 00:00:00 EDT 2014}
}
  • Conditions for entropy extremum of self-bound relativistic systems of particles, in stationary axisymmetric motion, are obtained under the following constraints: (i) The system is kept isolated in a geometrical sense, implying that the total mass--energy and total angular momentum, defined by the asymptotic behavior of the metric, are kept constant, (ii) the total number of particles is kept constant, and (iii) Einstein's constraint equations are imposed on a spacelike hypersurface. It is shown that if the system is in mechanical equilibrium, the total entropy is an extremum for all trial nonequilibrium configurations that satisfy the constraints and respect the symmetry,more » if and only if (i) Einstein's dynamical equations are satisfied, (ii) the temperature and the gravito-chemical potential, as seen from infinity, are constant, and (iii) the system is rigidly rotating. The proof does not depend on a particular functional expression for the mass of for the angular momentum; consequently, no related Lagrange multipliers have been used.« less
  • Required global energy transports determined from Nimbus-7 satellite net radiation measurements have been separated into atmospheric and oceanic components by applying a maximum entropy production principle to the atmospheric system. Strong poleward fluxes by the oceans in the Northern Hemisphere exhibit a maximum of 2.4 10[sup 15] W at 18[degrees]N, whereas maximum atmospheric transports are found at 37[degrees]N with a magnitude of 4.5 10[sup 15] W. These results are in good agreement with other published results. In the Southern Hemisphere, atmospheric transports are found to be considerably stronger than oceanic transports, and this finding corroborates findings based on other publishedmore » direct estimates. Maximum atmospheric energy transports are found at 37[degrees]S with a magnitude of 4.7 x 10[sup 15]W; two local oceanic transport maxima are shown at 18[degrees]S and 45[degrees]S with magnitudes of 1.3 x 10[sup 15] W and 1.1 x 10[sup 15] W, respectively. There is also evidence of net cross-equatorial transport in which the Southern Hemisphere oceans give rise to a net transfer of heat northward across the equator that exceeds a net transfer from Northern to Southern Hemisphere by the atmosphere. Since Southern Hemisphere results in this study should have the same degree of accuracy as in the Northern Hemisphere, these findings suggest that Southern Ocean transports are weaker than previously reported. A main implication of the study is that a maximum entropy production principle can serve as a governing rule on macroscale global climate, and in conjunction with conventional satellite measurements of the net radiation balance, provides a means to decompose atmosphere and ocean transports from the total transport field. Furthermore, the modeling methodology provides a possible means to partition the transports in a two-dimensional framework; this approach is tested on the separate ocean basins with qualified success. 59 refs., 4 figs., 2 tabs.« less
  • A variational principle has been found which is valid for irreversible processes, whether microscopic reversibility is obeyed or not, and beyond the region of linear response. A convenient general expression for entropy production is also found and the relation of entropy production to the solution of transport problems is discussed. (auth)