Eckart方程、Maxwellian迭代与散度型相对论因果理论
Eckart equations, Maxwellian iteration and Relativistic Causal Theories of Divergence type
AI总结：
本文在理性扩展热力学框架下研究散度型因果相对论理论，通过Maxwellian迭代收敛到Eckart方程的条件，并证明满足熵原理的系统均满足此条件，且在单原子和多原子气体中验证。
摘要：
我们在理性扩展热力学（RET）框架内，针对可压缩、可能稠密的气体，考虑一类一般的散度型因果相对论理论。我们要求该系统在Maxwellian迭代的第一步收敛到抛物型Eckart方程。这一要求意味着在三重张量在平衡态下评估时出现的两个系数之间存在一个约束。此外，对于给定的热状态方程和量热状态方程，以及给定的热导率、剪切粘度和体粘度，确定了产生张量。在第二部分中，我们证明，如果原始双曲系统满足RET的普遍原理，即可以使用主场以对称形式表示，则它总是满足先前的相容性条件。因此，任何满足熵原理且具有凸熵的散度型因果系统，在Maxwellian迭代中收敛到Eckart系统，即使我们在介观尺度上没有来自动力学理论的信息。所得结果在稀薄单原子和多原子气体的RET理论中进行了测试。
英文摘要：
We consider a general causal relativistic theory of divergence type in the framework of Rational Extended Thermodynamics (RET) for a compressible, possibly dense, gas. We require that the system converges in the Maxwellian iteration's first step to the parabolic Eckart equations. This requirement implies a constraint between the two coefficients present in the triple tensor evaluated at equilibrium. Moreover, the production tensor is determined for prescript thermal and caloric state equations and given heat conductivity, shear, and bulk viscosities. In the second part, we prove that if the original hyperbolic system satisfies the universal principles of RET, as can be put in the symmetric form using the \emph{main field}, it always satisfies the previous compatibility condition. Therefore any causal system of divergence type that satisfies the entropy principle with a convex entropy converges to the Eckart system in the Maxwellian iteration also when we have no information at the mesoscopic scale from the kinetic theory. The obtained results are tested on the RET theories of rarefied monatomic and polyatomic gases.
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