自由降落中的理想气体盒
Box of Ideal Gas in Free Fall
摘要：
本文研究了在任意弯曲时空中以中心4速度u^a自由下落的非相对论性理想气体的\textit{quantum}配分函数。当扰动能量本征值被适当考虑，我们发现，各种热力学量的修正包括一个非常具体的，次主导的条款，这是独立的\textit{kinematic}细节，如盒子尺寸和质量的粒子。这一项的特征是无量纲量，R =R_00 Λ^2，其中R_00=R_ab u^a u^b，Λ=β \hbar c，并且，非常有趣的是，它产生了熵和能量之间的齐次性2的欧拉关系--一个在黑洞热力学中很熟悉的关系。
英文摘要：
We study the \textit{quantum} partition function of non-relativistic, ideal gas in a (non-cubical) box falling freely in arbitrary curved spacetime with centre 4-velocity u^a. When perturbed energy eigenvalues are properly taken into account, we find that corrections to various thermodynamic quantities include a very specific, sub-dominant term which is independent of \textit{kinematic} details such as box dimensions and mass of particles. This term is characterized by the dimensionless quantity, Ξ=R_00 Λ^2, where R_00=R_ab u^a u^b and Λ=β\hbar c, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy -- a relation familiar from black hole thermodynamics.
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