基于互信息的有限数据复杂系统相变识别
Mutual Information as a Tool for Identifying Phase Transitions in Dynamical Complex Systems With Limited Data
摘要：
我们使用一个众所周知的模型（T。Vicsek等人，Phys Rev Lett 15，1226（1995）），用于群集以测试互信息作为用于检测有序-无序转变的工具，特别是当系统的观测有限时。我们表明，互信息是一个敏感的指标的相变的位置，在自然的无量纲参数的系统，我们已经确定。当仅跟踪少数粒子时，并且当仅位置和速度分量的子集可用时，互信息提供了比数据的磁化率更好的相变位置的测量。
英文摘要：
We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that mutual information is a sensitive indicator of the phase transition location, in terms of the natural dimensionless parameters of the system which we have identified. When only a few particles are tracked, and when only a subset of the positional and velocity components are available, mutual information provides a better measure of the phase transition location than the susceptibility of the data.
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