旋转中理想气体的Hessian几何
The Hessian geometry of the ideal gas in rotation
AI总结：
本文研究球形离心机中理想气体的Hessian几何，探讨其Gibbs态构成的指数族，并证明在高角速度极限下该几何与双曲空间等距的球面刚体Hessian几何可类比。
摘要：
我们研究与球形离心机中理想气体相关的Hessian几何。根据Souriau的理论，球面约束的理想气体存在热平衡和旋转平衡状态。这些被称为Gibbs态的状态构成了一个具有Euclidean旋转群作用的指数族。我们研究了其Hessian（Fisher-Rao）几何，并证明在角速度趋于无穷大的极限下，该几何可类比于球面刚体的Hessian几何，后者被证明与双曲空间等距。
英文摘要：
We study the Hessian geometry associated with an ideal gas in a spherical centrifuge. According to Souriau, a spherically confined ideal gas admit states of thermal and rotational equilibrium. These states, called Gibbs states, form an exponential family with an action of the Euclidean rotation group. We investigate its Hessian (Fisher-Rao) geometry and show that in the high angular velocity limit, the geometry can be compared to the Hessian geometry of a spherical rigid body which we show to be isometric to a hyperbolic space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
