热力学热力学第一定律的分析力学方法及变分方程组的构造
An Analytical Mechanics Approach to the First Law of Thermodynamics and Construction of a Variational Hierarchy
摘要：
本文提出了一种研究一维连续介质力学中有耗散的能量守恒方程的简便方法。这个过程是用来把这个非线性发展扩散方程转化为双曲型偏微分方程，具体地说，二阶拟线性波动方程。这一过程的直接含义是能量与耗散平衡的最小作用量原理的形成。相应的作用泛函使我们能够建立一个完整的热力学系统的分析力学：拉格朗日-哈密顿理论，运动积分，括号形式主义，和诺特定理。此外，我们反复应用我们的程序，并产生一个无限序列的联锁变分原理，变分层次，在每一个层次或迭代的最小作用量原理的全部含义可以再次显示。
英文摘要：
A simple procedure is presented to study the conservation of energy equation with dissipation in continuum mechanics in 1D. This procedure is used to transform this nonlinear evolution-diffusion equation into a hyperbolic PDE; specifically, a second order quasi-linear wave equation. An immediate implication of this procedure is the formation of a least action principle for the balance of energy with dissipation. The corresponding action functional enables us to establish a complete analytic mechanics for thermomechanical systems: a Lagrangian-Hamiltonian theory, integrals of motion, bracket formalism, and Noether's theorem. Furthermore, we apply our procedure iteratively and produce an infinite sequence of interlocked variational principles, a variational hierarchy, where at each level or iteration the full implication of the least action principle can be shown again.
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