The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than c. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds.

Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields — and further fields — are conveniently chosen from the moments of the kinetic theory of gases.

The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to c, the speed of light.

In extended thermodynamics symmetric hyperbolicity — and finite speeds — are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases.

粘性导热流体的纳维-斯托克斯-傅里叶理论提供了抛物线方程，从而预测无限的脉冲速度。自然地，这一特征使相对论热力学理论失去了资格，相对论热力学理论必须坚持有限速度，而且必须坚持小于c 的速度。事实证明，补救措施的尝试对于一种新的系统类型的热力学：扩展热力学具有启发性的重要性。该新理论具有对称双曲场方程，因此它提供了有限的脉冲速度。

扩展热力学是一个完整的理论体系，当热力学过程的梯度和速率变得更陡和更快时，其领域数量不断增加。这个层次结构的第一阶段是 14 场理论，它可能已经成为相对论者在许多应用中的有用工具。这 14 个场以及其他场可以方便地从气体动力学理论的矩中选择。

只有当字段的数量趋于无穷大时，层次结构才是完整的。在这种情况下，非相对论扩展热力学的脉冲速度趋于无穷大，而相对论扩展热力学的脉冲速度趋于c （光速）。

在扩展热力学中，熵密度的凹性暗示着对称双曲性和有限速度。对于特权熵密度（即非简并气体的其余框架的熵密度）而言，这在相对论热力学中仍然成立。