热力学与Action原理，热和引力（第2版）
Thermodynamics with an Action Principle, heat and gravitation (2nd version)
摘要：
应用于大气和恒星结构的水动力学和热力学的某些特征是令人困惑的：1。首先由拉普拉斯提出的关于我们的大气具有绝热温度分布的建议，在低层得到了证实，但是为什么它应该是这样的原因只能定性地理解。2.在水动力系统和引力的背景下，能量概念起作用的论点往往是有缺陷的，一些关于模型恒星结构稳定性的熟悉结果，首先在19世纪末提出，并在最现代的教科书中重复，也不完全令人信服。3.相对论热力学的标准处理方法不允许系统地处理混合物，例如理想气体与辐射的混合物。4.在应用广义相对论研究恒星结构时，质量的概念是不能令人满意的。有人建议，制定热力学作为一个行动的原则可能是一个合适的方法，通过对这些问题的新的调查。我们用作用量原理来表述理想气体的热力学，并研究理想气体与光子气体或热之间的相互作用。作用量原理提供了一个哈密顿泛函，这在传统的方法中是不可用的，在传统的方法中，熟悉的能量表达式没有操作意义。为了确定辐射在多大程度上影响了大气层的形状，我们研究了外部引力场中通常的多变大气层。提出了辐射平衡概念的一种新表述。
英文摘要：
Some features of hydro- and thermodynamics, as applied to atmospheres and to stellar structures, are puzzling: 1. The suggestion, first made by Laplace, that our atmosphere has an adiabatic temperature distribution, is confirmed for the lower layers, but the reason why it should be so is understood only qualitatively. 2. Arguments in which a concept of energy plays a role, in the context of hydro-thermodynamical systems and gravitation, are often flawed, and some familiar results concerning the stability of model stellar structures, first advanced at the end of the 19th century and repeated in the most modern textbooks, are less than completely convincing. 3. The standard treatment of relativistic thermodynamics does not allow for a systematic treatment of mixtures, such as the mixture of a perfect gas with radiation. 4. The concept of mass in applications of general relativity to stellar structure is unsatisfactory. It is proposed that a formulation of thermodynamics as an action principle may be a suitable approach to adopt for a new investigation of these matters. We formulate thermodynamics of ideal gases in terms of an action principle and study the interaction between an ideal gas and the photon gas, or heat. The action principle provides a hamiltonian functional, not available in traditional approaches where familiar expressions for the energy have no operative meaning. The usual polytropic atmosphere in an external gravitational field is examined, in order to determine to what extent it is shaped by radiation. A new formulation of the concept of radiative equilibrium is proposed.
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