On the problem of the minimum entropy production in the nonequilibrium stationary state

Martyushev, L. M.; Nazarova, A S; Селезнев, В. Д.

doi:10.1088/1751-8113/40/3/002

Cited by 51 publications

(54 citation statements)

References 22 publications

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“…However, there were attempts to use this principle for finding the spatial distribution of physical quantities (i.e., to extend the application of the principle to the so-called integral case) (see, e.g., [2]). Nevertheless, such an extended understanding of the principle is, for the most part, wrong (see, for example, [13]). …”

Section: Prigogine's and Ziegler's Principlementioning

confidence: 99%

“…Then, by involving the heat balance equation, we can calculate temporal and spatial distributions of the temperature in the rod subject to imposed constraints. There can be a lot of constraints, so, in principle, any behavior of the entropy production can be obtained as early as at this second stage [13]. Another example is from chemistry.…”

Section: The Range Of Mepp Applicabilitymentioning

confidence: 99%

See 1 more Smart Citation

Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

Martyushev

2013

Entropy

153

155

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Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings). The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress) in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.

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Section: Prigogine's and Ziegler's Principlementioning

confidence: 99%

Section: The Range Of Mepp Applicabilitymentioning

confidence: 99%

Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

Martyushev

2013

Entropy

153

155

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“…It was formulated by Prigogine in 1947 [1] and successively different authors, including Prigogine himself and his coworkers, tried to generalize it and to put forth new examples and new areas of application for the principle: for example it has been employed in chemistry, biology, ecology and, obviously, in engineering sciences (see, e.g., [2] and references therein). In addition, due to these large number of applications, different statements about the principle, its validity and applicability have been given in the literature.…”

Section: Introductionmentioning

confidence: 99%

Entropy Production in the Theory of Heat Conduction in Solids

Zullo

2016

Entropy

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The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine's minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We suggest a characterization of the evolution of the entropy production of the system through the generalized Fourier modes, showing that they are the only states with a time independent entropy production. The variational approach and a Lyapunov functional of the temperature, monotonically decreasing with time, are discussed. We describe the analytic properties of the entropy production as a function of time in terms of the generalized Fourier coefficients of the system. Analytical tools are used throughout the paper and numerical examples will support the statements.

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“…The problem of the validity (or invalidity) of the minimum entropy production density law in a stationary state of a system may be discussed from different points of view [28]. The aim of the present paper was the analysis of this problem in connection with the symmetry properties of the kinetic coefficients.…”

Section: Discussionmentioning

confidence: 98%