论文标题
快速慢性哈密顿系统的二阶扩展和热力学解释
Second-order asymptotic expansion and thermodynamic interpretation of a fast-slow Hamiltonian system
论文作者
论文摘要
本文包括对确定性快速系统的选定平均和尺寸缩小技术的简短调查。该调查包括经典技术，例如WKB近似或平均方法以及现代技术，例如通用形式主义。本文的主要部分结合了其中一些技术的想法，并解决了为快速慢的汉密尔顿系统的缓慢自由度（DOF）得出减少系统的问题。在第一部分中，我们使用弱收敛技术和两尺度的收敛性得出了快速慢系统的平均演化的渐近扩展。在第二部分中，我们确定可以使用第一部分的结果将可以解释为系统温度和熵的数量，并将这些数量扩展到二阶。结果为快速慢系统的热力学解释提供了新的见解。
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging method, as well as modern techniques, such as the GENERIC formalism. The main part of this article combines ideas of some of these techniques and addresses the problem of deriving a reduced system for the slow degrees of freedom (DOF) of a fast-slow Hamiltonian system. In the first part, we derive an asymptotic expansion of the averaged evolution of the fast-slow system up to second-order, using weak convergence techniques and two-scale convergence. In the second part, we determine quantities which can be interpreted as temperature and entropy of the system and expand these quantities up to second-order, using results from the first part. The results give new insights into the thermodynamic interpretation of the fast-slow system at different scales.
