论文标题
共形渔民信息指标与扭转
Conformal Fisher information metric with torsion
论文作者
论文摘要
我们考虑通过Fisher Information指标的共形转换产生的参数歧管扭转，并将其定义为用于广泛物理系统的信息几何形状。扭转可用于区分概率分布函数，否则具有相同的标量曲率，因此定义了相似的几何形状。在热力学几何形状的背景下，我们的结构产生了一个新的标量 - 在歧管上定义的扭转标量，同时保留了与其他标量量相关的已知物理特征。我们在Van der Waals和Curie-Weiss模型的背景下进行分析。在这两种情况下，扭转标量在Spinodal曲线上都有非微不足道的行为。
We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar - the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie-Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve.
