TY - JOUR
T1 - The Physical Entropy of Single Conservation Laws
AU - Lei , Gongyan
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, Entropy, Entropy production.
AB - <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>