论文标题
将复杂网络连接到非添加熵
Connecting complex networks to nonadditive entropies
论文作者
论文摘要
Boltzmann-Gibbs统计力学可满足于多种系统。但是，对于涉及强大时空纠缠的复杂系统而言，它失败了。它基于非addive $ Q $ entropies的概括可以充分处理大量此类系统。我们在这里显示比例不变的网络属于此类。我们在数值上研究了具有加权链接的地理位置上的$ d $维度，并在其准平台状态下显示其每个站点的“能量”分布。我们的结果强烈暗示了随机几何问题与广义恒温器中的一类热问题之间的对应关系。 Boltzmann-Gibbs的指数因子通常用其$ Q $归属化代替，当非本地效应消失时，$ q = 1 $限制以$ q = 1 $的限制恢复。目前的联系应在两个研究领域进行跨施用实验。
Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a $d$-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann-Gibbs exponential factor is generically substituted by its $q$-generalisation, and is recovered in the $q=1$ limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.
