论文标题
信息几何学和黑洞热力学中的大地测量机制
Mechanics of geodesics in Information geometry and Black Hole Thermodynamics
论文作者
论文摘要
在本文中，我们将讨论信息几何形状中的测量学理论以及在天体物理学中的应用。我们将研究信息几何形状中的梯度流如何描述大地学，通过引入约束来探索相关机制，并将我们的理论应用于高斯模型和黑洞热力学。因此，我们证明了梯度流的变形如何导致更通用的兰德斯 - 芬斯勒指标，描述源自约束的汉密尔顿力学，并通过规范变换证明二元性。我们还验证了高斯模型变形的理论，并描述了Kerr和Reissner-Nordström黑洞的平坦指标的动态演化。
In this article we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers-Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner-Nordström black holes.
