平衡态热力学的Hamiltonian形式:从Gibbs变分原理到分析热力学

A Hamiltonian Formulation of Equilibrium Thermodynamics: From Gibbs Variational Principle to Analytical Thermodynamics

用分析力学的方法研究平衡态热力学.证明了平衡态热力学中的基本Poisson括号成立.借助于Gibbs变分原理,讨论了平衡态热力学中热力学量的正则变换.得到了热力学正则变换的4种形式.在分析热力学中同样提出了化"准Hamiltonian"为压强或容积的正则变换技术.作为应用正则变换的实例,讨论了理想气体并得到了简明的结果.

Analytical thermodynamics provides a study of thermodynamics through the methods of analytical mechanics. With it the canonical equations in equilibrium thermodynamics, i.e. the basic Poisson's brackets can be proved. The major objective is the discussion of canonical transformation of thermodynamical quantities in equilibrium thermodynamics by the Gibbs variational principle. These canonical transformations can take four forms. The quasi-Hamilton-Jacobi equation can be expressed and the canonical transformation technique, viz. that of changing a quasi-Hamiltonian into a pressure or a volume in equilibrium thermodynamics is performed. As an example of applying the canonical transformation, ideal gas is discussed giving clear and distinct results.