论文标题
具有非零热通量的相对论气体的可变性条件
Realizability conditions for relativistic gases with a non-zero heat flux
论文作者
论文摘要
这项工作引入了对最小值的限制，而在存在非零热通量的情况下，相对论气体的能量可以假设。这种限制是由粒子分布函数的非阴性产生的，并且可以通过解决汉堡矩问题来找到。在零热通量的情况下，看到所得的限制可恢复taub不等式，但是如果考虑非零热通量，则更严格。这些结果表明，为了使分布函数为非负，（i）气体的能量必须大于最小阈值； （ii）另一方面，热通量具有由能量和压力张量确定的最大值； （iii）存在相对论状态方程的绝热指数$γ$的上限，并且在存在热通量和压力各向异性的情况下，限制降低，渐近为$γ= 1 $。后一点意味着状态的综合方程与相对论气体正式不兼容，显示出热通量，除了某些气体状态。
This work introduces a limitation on the minimum value that can be assumed by the energy of a relativistic gas in the presence of a non-zero heat flux. Such a limitation arises from the non-negativity of the particle distribution function, and is found by solving the Hamburger moment problem. The resulting limitation is seen to recover the Taub inequality in the case of a zero heat flux, but is more strict if a non-zero heat flux is considered. These results imply that, in order for the distribution function to be non-negative, (i) the energy of a gas must be larger than a minimum threshold; (ii) the heat flux, on the other hand, has a maximum value determined by the energy and the pressure tensor; and (iii) there exists an upper limit for the the adiabatic index $Γ$ of the relativistic equation of state, and that limit decreases in the presence of a heat flux and pressure anisotropy, asymptoting to a value $Γ= 1$. The latter point implies that the Synge equation of state is formally incompatible with a relativistic gas showing a heat flux, except in certain gas states.
