用Gauss和Doll张量分子动力学计算Sadi卡诺循环的热力学熵
Thermodynamic Entropy from Sadi Carnot's Cycle using Gauss' and Doll's-Tensor Molecular Dynamics
摘要：
卡诺的四部分理想气体循环包括等温和绝热膨胀和压缩。分析这个循环为统计热力学提供了基本的基础。我们从教学的角度探讨循环，以促进理解宏观热力学熵，态函数与热能的变化。从另一种微观观点来看，哈密顿量${\cal H}(q,p)$是能量，熵是与宏观状态相关的相空间体积$Ω$（的对数）。我们将两种新形式的哈密顿力学应用于卡诺循环：[1]等温段的高斯等动力学和[2]等熵绝热段的多尔张量。我们探讨的等效性的微观和宏观观点卡诺循环简单的流体在这里，开始与理想的克努森气体和扩展的分析，以一个原型的简单流体。
英文摘要：
Carnot's four-part ideal-gas cycle includes both isothermal and adiabatic expansions and compressions. Analyzing this cycle provides the fundamental basis for statistical thermodynamics. We explore the cycle here from a pedagogical view in order to promote understanding of the macroscopic thermodynamic entropy, the state function associated with thermal energy changes. From the alternative microscopic viewpoint the Hamiltonian ${\cal H}(q,p)$ is the energy and entropy is the (logarithm of the) phase-space volume $Ω$ associated with a macroscopic state. We apply two novel forms of Hamiltonian mechanics to Carnot's Cycle: [1] Gauss' isokinetic mechanics for the isothermal segments and [2] Doll's Tensor for the isentropic adiabatic segments. We explore the equivalence of the microscopic and macroscopic views of Carnot's cycle for simple fluids here, beginning with the ideal Knudsen gas and extending the analysis to a prototypical simple fluid.
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