Limits of classical constitutive laws such as Fourier and Navier–Stokes equations are discovered since decades. However, the proper extensions—generalizations of these—are not unique. They differ in the underlying physical principles and in modeling capabilities. In this paper, two different theories are discussed and compared to each other, namely the kinetic theory-based rational extended thermodynamics (RET) and non-equilibrium thermodynamics with internal variables (NET-IV). First, the paper starts with the case of rigid heat conductors summarizing the result achieved so far. Then, a typical example of compressible bodies is shown by presenting the first generalization for rarefied gases, called Meixner’s theory. It is further extended using generalized entropy current in the framework of NET-IV. It is shown how its structure is related to RET and how the compatibility between them can be acquired.

几十年来，人们发现了诸如Fourier和Navier-Stokes方程之类的经典本构法的极限。但是，适当的扩展名（它们的概括）并不是唯一的。它们在基本物理原理和建模功能方面有所不同。本文讨论并比较了两种不同的理论，即基于动力学理论的有理扩展热力学（RET）和带有内部变量的非平衡热力学（NET-IV）。首先，本文从刚性导热体的情况开始，总结了迄今为止所取得的成果。然后，通过介绍稀有气体的第一个概括（称为Meixner理论），显示了可压缩物体的典型示例。在NET-IV框架中使用广义熵电流对其进行了进一步扩展。