[论文解读] Thermodynamics as a multistep relaxation process and the role of observables in different scales of quantities

V. P. Maslov|arXiv (Cornell University)|Mar 21, 2013

Advanced Thermodynamics and Statistical Mechanics参考文献 1被引用 6

一句话总结

本文将热力学重新解释为在宏观、微观和纳米尺度上的多步弛豫过程，引入了分子、二聚体和类似玻色子凝聚态的可观测量。通过多 polylogarithmic 方程推导出对应状态定律，并预测了在无分子间吸引力的理想气体中发生相变，使用 Zeno 线和二聚体形成阈值，对汞和甲烷的预测具有定量一致性。

ABSTRACT

In the first part of the paper, we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length, and also the relationship between these observable quantities. The concept of the number of degrees of freedom, which relates the observable quantities listed above, is generalized to the case of low temperatures. An analogy between the creation and annihilation operators for pairs (dimers) and the creation and annihilation operators for particles (molecules) is carried out. A generalization of the concept of a Bose condensate is introduced for classical molecules as an analog of an ideal liquid (without attraction). The negative pressure in the liquid is treated as holes (of exciton type) in the density of the Bose condensate. The phase transition gas-liquid is calculated for an ideal gas (without attraction). A comparison with experimental data is carried out. In the other part of the paper, we introduce the concept of new observable quantity, namely, of a pair (a dimer), as a result of attraction between the nearest neighbors. We treat in a new way the concepts of Boyle temperature $T_B$ (as the temperature above which the dimers disappear) and of the critical temperature $T_c$ (below which the trimers and clusters are formed). The equation for the Zeno line is interpreted as the relation describing the dependence of the temperature on the density at which the dimers disappear. We calculate the maximal density of the liquid and also the maximal density of the holes. The law of corresponding states is derived as a result of an observation by a macrodevice which cannot distinguish between molecules of distinct gases, theoretical and experimental data are compared, observations in three scales, macro, micro, and nano, are studied.

研究动机与目标

• 通过多步弛豫过程，统一宏观热力学可观测量与微观和纳米尺度粒子动力学。
• 将玻色凝聚的概念推广至经典分子，将负压视为凝聚态中的空穴激发。
• 定义新的可观测量如二聚体和团簇，并将其与波义耳温度和临界温度相关联。
• 从宏观观测极限出发推导对应状态定律，并将理论预测与实验数据进行比较。
• 利用 Zeno 线和二聚体消失条件，对无吸引力的理想气体中的相变进行建模。

提出的方法

• 引入宏观、微观和纳米尺度的可观测量：宏观仪器测量密度和温度；微观仪器测量分子半径和自由程；纳米尺度的可观测量为二聚体。
• 使用二聚体和分子的产生与湮灭算符，类比于量子场论。
• 应用多 polylogarithmic 函数（Li_s(y)）和 zeta 函数，以模拟粒子分布并推导等容方程。
• 将 Zeno 线定义为二聚体消失的轨迹，使用多 polylogarithm 比值等于临界值的条件。
• 通过方程 (105) 和 (106) 构建等容线和等温线，利用依赖于 γ 的函数将压强、体积和温度关联起来。
• 应用 Wiener 不确定性原理，解释非垂直的气-液相变及临界指数异常。

实验结果

研究问题

• RQ1 如何将热力学重新解释为在宏观、微观和纳米尺度上的多步弛豫过程？
• RQ2 二聚体形成在定义理想气体中波义耳温度和临界温度方面起什么作用？
• RQ3 Zeno 线如何与二聚体的消失及类液行为的出现相关联？
• RQ4 能否从宏观观测限制和统计力学出发推导出对应状态定律？
• RQ5 polylogarithmic 函数和 zeta 函数如何在无分子间吸引力的情况下模拟状态方程和相变？

主要发现

• 汞的分子最大压缩因子 Z_m 在 γ_min = 0.1 时达到 0.4，与临界压缩因子 Z_c 一致，证实了该模型对汞的自洽性。
• Zeno 线被推导为二聚体消失的条件，得到方程：Li_{γ+2}(y_z)/Li_{γ+1}(y_z) · V_m/N_c · ζ(γ+1)/ζ(γ+2) = 1。
• 高密度下的等容线被证明近乎直线，且所有等容线均通过 Zeno 线和 P_s = 1 上的点 Z_0 = 1/ρ。
• 汞（图 12）和甲烷（图 13）的理论等温线与实验数据在 Wiener 原理和粗略宏观仪器的不确定度范围内一致。
• 由于粘度和测量不确定度，汞的气-液相变发生在 T = 1473 K 沿斜线进行，而非垂直转变。
• 该模型预测，当 Z < 0.4（例如范德瓦尔斯气体）时，对于不可区分的粒子，会发生向液相的相变，与对应状态定律一致。