Variational principles of dissipative systems

Gafiichuk, V. V.; Lubashevskii, I. A.

doi:10.1007/bf01095874

Cited by 2 publications

(1 citation statement)

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“…For example, linear problems can easily be reduced to a potential form. However, this does not mean that the extremal principle does not exist for non-potential problems [94][95][96][97]. A variety of "recipes" for constructing extremal principles are proposed in [98][99][100].…”

Section: Extremal Principles For Dissipative Systems Not Directly Rel...mentioning

confidence: 99%

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

Donskoy

2022

Energies

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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.

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