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On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review

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  • Igor Donskoy

    (Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia)

Abstract

A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined. Examples are shown in which the mechanical use of entropy production-based principles turns out to be inefficient and even contradictory. The main problem of extremal principles in the theory of irreversible processes is the impossibility of their generalization, often even within the framework of a class of problems. Alternative extremal formulations are considered: variational principles for heat and mass transfer equations and other dissipative systems. Several extremal principles are singled out, which make it possible to simplify the numerical solution of the initial equations. Criteria are proposed that allow one to classify extremal principles according to their areas of applicability. Possible directions for further research in the search for extremal principles in the theory of irreversible processes are given.

Suggested Citation

  • Igor Donskoy, 2022. "On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review," Energies, MDPI, vol. 15(19), pages 1-23, September.
  • Handle: RePEc:gam:jeners:v:15:y:2022:i:19:p:7152-:d:928433
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    References listed on IDEAS

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    1. Lucia, Umberto, 2014. "Entropy generation: Minimum inside and maximum outside," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 61-65.
    2. Pagonabarraga, I. & Pérez-Madrid, A. & Rubí, J.M., 1997. "Fluctuating hydrodynamics approach to chemical reactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 205-219.
    3. Yuri S. Popkov, 2020. "Equilibria and Stability of One Class of Positive Dynamic Systems with Entropy Operator: Application to Investment Dynamics Modeling," Mathematics, MDPI, vol. 8(6), pages 1-15, May.
    4. D. Lebiedz & J. Unger, 2016. "On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 22(2), pages 87-112, March.
    5. Lucia, Umberto, 2009. "Irreversibility, entropy and incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4025-4033.
    6. Bochkov, G.N. & Kuzovlev, Yu.E., 1981. "Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(3), pages 443-479.
    7. Michael H. Peters, 2021. "Nonequilibrium Entropy Conservation and the Transport Equations of Mass, Momentum, and Energy," Energies, MDPI, vol. 14(8), pages 1-8, April.
    8. Kong, Xinlei & Wang, Zhongxin & Wu, Huibin, 2022. "Variational integrators for forced Lagrangian systems based on the local path fitting technique," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    9. Bochkov, G.N. & Kuzovlev, Yu.E., 1981. "Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(3), pages 480-520.
    10. Kolenda, Z. & Donizak, J. & Hubert, J., 2004. "On the minimum entropy production in steady state heat conduction processes," Energy, Elsevier, vol. 29(12), pages 2441-2460.
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