We address the link between the controllability or observability of a stochastic complex system and concepts of information theory. We show that the most influential degrees of freedom can be detected without acting on the system, by measuring the time-delayed multi-information. Numerical and analytical results support this claim, which is developed in the case of a simple stochastic model on a graph, the so-called voter model. The importance of the noise when controlling the system is demonstrated, leading to the concept of control length. The link with classical control theory is given, as well as the interpretation of controllability in terms of the capacity of a communication canal.

我们解决了随机复杂系统的可控制性或可观察性与信息论概念之间的联系。我们表明，通过测量延时的多信息，可以在不影响系统的情况下检测出最具影响力的自由度。数值和分析结果支持该要求，该要求是在图形上的简单随机模型（即所谓的选民模型）的情况下提出的。演示了控制系统时噪声的重要性，从而得出了控制长度的概念。给出了与经典控制理论的联系，并根据通信渠道的容量对可控制性进行了解释。