Metzig Cornelia, Colijn Caroline
Business School, Imperial College London, London SW7 2AZ, UK.
School of Electronic Engineering and Computer Science, Queen Mary University, London E1 7NS, UK.
Entropy (Basel). 2020 Mar 10;22(3):312. doi: 10.3390/e22030312.
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of constant size, which contains exit of balls and urns (or nodes and edges for the network case). Knowing mean size (degree) and turnover rate, the power law exponent and exponential cutoff can be derived. Our results are confirmed by simulations and by computation of exact probabilities. We also apply this entropy method to reproduce existing results like the Maxwell-Boltzmann distribution for the velocity of gas particles, the Barabasi-Albert model and multiplicative noise systems.
我们提出了一种方法，通过最大化吉布斯 - 香农熵来推导系统的稳态规模分布和网络的度分布。我们将此方法应用于固定规模系统的偏好依附型算法，该算法包含球与瓮（或网络情形下的节点与边）的退出。已知平均规模（度）和周转率，即可推导出幂律指数和指数截断。我们的结果通过模拟以及精确概率的计算得到了证实。我们还应用这种熵方法来重现现有结果，如气体粒子速度的麦克斯韦 - 玻尔兹曼分布、巴拉巴西 - 阿尔伯特模型和乘性噪声系统。
