@Article{JCM-16-5,
author = {Lei, Gongyan},
title = {The Physical Entropy of Single Conservation Laws},
journal = {Journal of Computational Mathematics},
year = {1998},
volume = {16},
number = {5},
pages = {437--444},
abstract = {<p style="text-align: justify;">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&#39;s famous E-condition can be explained successfully in physics.</p>},
issn = {1991-7139},
doi = {https://doi.org/1998-JCM-9173},
url = {https://global-sci.com/article/85707/the-physical-entropy-of-single-conservation-laws}
}