论文标题
高斯随机场中的曲率效应
The Curvature Effect in Gaussian Random Fields
论文作者
论文摘要
随机场模型是随机复合系统研究中使用的数学结构。在本文中，我们使用第一和第二个基本形式（Fisher Information矩阵）计算高斯随机场歧管的形状操作员。使用马尔可夫链蒙特卡洛技术，我们模拟了这些随机场的动力学，并计算了参数空间的高斯曲率，从而分析了该数量沿相变的方式如何变化。在模拟过程中，我们观察到了一种意外的现象，我们称为\ emph {曲率效应}，这表明当系统熵显着增加/减少时，在基础参数空间中发生了高度不对称的几何变形。这种不对称模式与滞后的出现有关，导致沿动力学的固有箭头。
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher information matrices). Using Markov Chain Monte Carlo techniques, we simulate the dynamics of these random fields and compute the Gaussian curvature of the parametric space, analyzing how this quantity changes along phase transitions. During the simulation, we have observed an unexpected phenomenon that we called the \emph{curvature effect}, which indicates that a highly asymmetric geometric deformation happens in the underlying parametric space when there are significant increase/decrease in the system's entropy. This asymmetric pattern relates to the emergence of hysteresis, leading to an intrinsic arrow of time along the dynamics.
