Volume 16, Issue 5
The Physical Entropy of Single Conservation Laws
DOI:

J. Comp. Math., 16 (1998), pp. 437-444

Published online: 1998-10

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• Abstract

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law $\partial_{t} u + \partial_{x} f(u) = 0$, if the flux function $f (u)$ is convex (or concave), then, the physical entropy is $S = -f (u)$; Furthermore, if we assume this result can be generalized to any $f (u)$ with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

• Keywords

Conservation laws Entropy Entropy production

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@Article{JCM-16-437, author = {}, title = {The Physical Entropy of Single Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {5}, pages = {437--444}, abstract = { By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law $\partial_{t} u + \partial_{x} f(u) = 0$, if the flux function $f (u)$ is convex (or concave), then, the physical entropy is $S = -f (u)$; Furthermore, if we assume this result can be generalized to any $f (u)$ with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9173.html} }
TY - JOUR T1 - The Physical Entropy of Single Conservation Laws JO - Journal of Computational Mathematics VL - 5 SP - 437 EP - 444 PY - 1998 DA - 1998/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9173.html KW - Conservation laws KW - Entropy KW - Entropy production AB - By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law $\partial_{t} u + \partial_{x} f(u) = 0$, if the flux function $f (u)$ is convex (or concave), then, the physical entropy is $S = -f (u)$; Furthermore, if we assume this result can be generalized to any $f (u)$ with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.
Gong-yan Lei. (1970). The Physical Entropy of Single Conservation Laws. Journal of Computational Mathematics. 16 (5). 437-444. doi:
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