Entropy-conserving numerical fluxes are a cornerstone of modern high-order entropy-dissipative discretizations of conservation laws. In addition to entropy conservation, other structural properties mimicking the continuous level such as pressure equilibrium and kinetic energy preservation are important. This note proves that there are no numerical fluxes conserving (one of) Harten's entropies for the compressible Euler equations that also preserve pressure equilibria and have a density flux independent of the pressure. This is in contrast to fluxes based on the physical entropy, where even kinetic energy preservation can be achieved in addition.

翻译：以通气为目的的数字通量是保护法中现代高序对流分解法的基石。除了保护酶外,其他结构特性也与压力平衡和动能节能等连续水平相仿也很重要。本说明证明,对于压缩的Euler方程式来说,没有数字通量保存(其中之一)哈顿的动能节能,这也保持了压力平衡,且其密度通量与压力无关。这与基于物理对流的通量形成对照,在这种通量之外,甚至动能节能也能够实现。