Evolution of Conditional Entropy for Diffusion Dynamics on Graphs
Samuel Koovely, Alexandre Bovet
图形上扩散过程的建模是许多网络科学和机器学习方法的基础。 最近采用了基于网络扩散的熵措施,以调查这些过程的可逆性和建模系统的多样性。 虽然关于它们稳定状态的结果是众所周知的,但关于它们的时间演变的确切结果很少。 在这里,我们在图中介绍热扩散的条件熵。 我们证明这种熵测量满足了热力学第一和第二定律,从而提供了对网络上扩散动力学的物理解释。 我们概述了一个数学框架,在连续时间马尔可夫链和信息理论中将扩散和条件熵进行上下背景。 此外,我们在完整、路径和圆曲图上获得其演变的明确结果,以及 Erdös-Rényi 图的均场近似值。 我们还为一般网络获得渐近结果。 最后,我们实验演示了条件熵在随机图上扩散的几个特性,例如Watts-Strogatz模型。
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs. We demonstrate that this entropi...