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Non-equilibrium diffusion in a particle system and the correspondence to understanding the propagation of public opinion
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2021-06-08 , DOI: 10.1007/s11071-021-06597-8
Peng Wang , Feng-Chun Pan , Jie Huo , Xu-Ming Wang

A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker–Planck equation by the Kramers–Moyal expansion. The solution of this equation exhibits some non-equilibrium phenomena. In the beginning the distribution curve of velocity/energy takes on a random oscillation, and then a near-equilibrium distribution described by the Boltzmann distribution is gradually established. However, a spike appears on the distribution curve and breaks this stable distribution. The spike moves in the direction of velocity/energy decreasing and is nonlinearly enlarged so as to sustain. The final distribution is a sharp peak formed by a monotonically ascending segment and a monotonically descending one. The calculating results of the statistical quantities demonstrate that the process is a sub-diffusion, and the spike originates from the correlation between noise and space. Two basic definitions are suggested to map the observations in this physical system to a social system to understand the propagation of public opinion or message, i.e., the generalized displacement is defined as the quantity of information carried by the opinion particle, and the velocity is defined as the sensitivity of the opinion particle to an event.



中文翻译:

粒子系统中的非平衡扩散与理解舆论传播的对应关系

建议使用朗之万方程来描述由相关高斯白噪声以及由临界速度界定的正负阻尼驱动的系统。该方程可以通过 Kramers-Moyal 展开式转化为 Fokker-Planck 方程。该方程的解表现出一些非平衡现象。开始时速度/能量的分布曲线呈随机振荡,然后逐渐建立由玻尔兹曼分布描述的近平衡分布。然而,分布曲线上出现了一个尖峰,打破了这个稳定的分布。尖峰沿速度/能量减小的方向移动,并非线性放大以维持。最终分布是由单调上升段和单调下降段形成的尖峰。统计量的计算结果表明,该过程是一个子扩散过程,尖峰源于噪声与空间的相关性。提出了两个基本定义来将这个物理系统中的观察映射到社会系统以理解舆论或消息的传播,即广义位移定义为舆论粒子携带的信息量,定义速度作为意见粒子对事件的敏感性。

更新日期:2021-06-08
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