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 -

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.