全局平衡至 $\mathcal{O}(\hbar^2)$ 阶：伪规范歧义、麦克斯韦关系与热力学一致性
Global equilibrium at order $\mathcal{O}(\hbar^2)$: pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency
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中文总结 AI 辅助
该研究在旋转和加速的全局平衡中，将量子修正纳入至二阶，发现质壳条件被修正，并证明动力学伪规范满足麦克斯韦关系，而其他伪规范不满足，推荐用于自旋流体动力学。
中文摘要 AI 辅助
我们研究具有旋转和加速度的全局热力学平衡中的大质量自旋-$1/2$ 玻尔兹曼粒子，并一致地纳入直至 $\mathcal{O}(\hbar^2)$ 阶的量子修正。对于这样的系统，流体速度成为独立的热力学变量，基本热力学关系需要扩展。采用维格纳函数形式，我们证明标准质壳条件 $k^2 = m^2$ 在 $\mathcal{O}(\hbar^2)$ 阶被与热涡度二次方相关的贡献所修正。结合这一修正的质壳约束，我们推导了（净）粒子数流、能量-动量张量、自旋流张量以及相关的热力学量，在动力学、正则和 de Groot--van Leeuwen--van Weert (GLW) 伪规范中。我们明确证明，虽然全局量（如总粒子数或总能量）不依赖于伪规范的选择，但局部量（如粒子数密度或能量密度）是伪规范依赖的。然后我们检查每种伪规范中的热力学关系，并证明热力学一致性要求热力学麦克斯韦关系得到满足。我们发现这些关系在动力学理论伪规范中成立，而在正则和 GLW 伪规范中通常被违反。这些发现表明，在自旋流体动力学等应用中，优先使用动力学理论伪规范。
英文摘要
We study massive spin-$1/2$ Boltzmann particles in global thermodynamic equilibrium with rotation and acceleration, consistently including quantum corrections up to order $\mathcal{O}(\hbar^2)$. For such a system, the fluid velocity becomes an independent thermodynamic variable and fundamental thermodynamic relations have to be extended. Employing the Wigner-function formalism, we show that the standard mass-shell condition $k^2 = m^2$ is modified at order $\mathcal{O}(\hbar^2)$ by contributions quadratic in the thermal vorticity. Incorporating this modified mass-shell constraint, we derive the (net) particle-number current, energy-momentum tensor, spin-current tensor, and associated thermodynamic quantities in the kinetic, canonical, and de Groot--van Leeuwen--van Weert (GLW) pseudo-gauges. We explicitly demonstrate that, while global quantities, like the total particle number or total energy, are independent of the choice of pseudo-gauge, local quantities, like the particle-number density or the energy density, are pseudo-gauge dependent. We then examine the thermodynamic relations in each pseudo-gauge and demonstrate that thermodynamic consistency requires that the thermodynamic Maxwell relations are satisfied. We find that these relations hold in the kinetic-theory pseudo-gauge, whereas they are in general violated in the canonical and GLW pseudo-gauges. These findings suggest a preference for using the kinetic-theory pseudo-gauge in applications such as spin hydrodynamics.
发表机构
- Institut für Theoretische Physik, Johann Wolfgang Goethe–Universität（法兰克福歌德大学理论物理研究所）
- Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）
- Helmholtz Research Academy Hesse for FAIR（黑森FAIR亥姆霍兹研究院）
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