纳米热力学导论：非均相和有限尺寸体系的热平衡
An introduction to nanothermodynamics: Thermal equilibrium for heterogeneous and finite-sized systems
摘要：
小系统热力学理论最初是为了将热力学热力学定律扩展到纳米尺度而发展起来的。在这里，我们回顾这一“纳米热力学”，并强调它如何也适用于大型系统，细分成一个异质分布的内部子系统，我们称之为“区域”。“我们强调，大多数系统的真正热平衡通常要求这些区域处于完全开放的广义系综中，区域大小的分布不受外部约束，我们称之为“纳米正则”系综。我们专注于纳米热力学如何影响特定模型的统计力学。一个例子是一个理想气体的原子在一个大的体积，细分成一个整体的小区域的可变体积，与单独的区域包含的原子是可区分的，从其他地区。结合这些细分的区域产生正确的混合熵，避免吉布斯悖论，而不诉诸于半经典粒子的宏观量子对称性。其他模型基于Ising类自旋（二元自由度），在一维中解析求解，使其成为统计物理学入门课程的合适示例。一个关键的结果是量化熵的净增加时，大系统细分成小区域的可变大小。另一个结果是显示在nanocanonical系综中的两态模型和在正则系综中的三态模型的平衡性质的相似性。因此，涌现现象可能会改变微观模型的热行为，正确的系综是准确预测所必需的。
英文摘要：
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide into a heterogeneous distribution of internal subsystems that we call "regions." We emphasize that the true thermal equilibrium of most systems often requires that these regions are in the fully-open generalized ensemble, with a distribution of region sizes that is not externally constrained, which we call the "nanocanonical" ensemble. We focus on how nanothermodynamics impacts the statistical mechanics of specific models. One example is an ideal gas of indistinguishable atoms in a large volume that subdivides into an ensemble of small regions of variable volume, with separate regions containing atoms that are distinguishable from those in other regions. Combining such subdivided regions yields the correct entropy of mixing, avoiding Gibbs paradox without resorting to macroscopic quantum symmetry for semi-classical particles. Other models are based on Ising-like spins (binary degrees of freedom), which are solved analytically in one-dimension, making them suitable examples for introductory courses in statistical physics. A key result is to quantify the net increase in entropy when large systems subdivide into small regions of variable size. Another result is to show similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for accurate predictions.
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