Meijers Matthijs, Ito Sosuke, Ten Wolde Pieter Rein
NWO Institute AMOLF, 1098 XG Amsterdam, The Netherlands.
Universal Biology Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan.
Phys Rev E. 2021 Jan;103(1):L010102. doi: 10.1103/PhysRevE.103.L010102.
Recent experiments have indicated that many biological systems self-organize near their critical point, which hints at a common design principle. While it has been suggested that information transmission is optimized near the critical point, it remains unclear how information transmission depends on the dynamics of the input signal, the distance over which the information needs to be transmitted, and the distance to the critical point. Here we employ stochastic simulations of a driven two-dimensional Ising system and study the instantaneous mutual information and the information transmission rate between a driven input spin and an output spin. The instantaneous mutual information varies nonmonotonically with the temperature but increases monotonically with the correlation time of the input signal. In contrast, there exists not only an optimal temperature but also an optimal finite input correlation time that maximizes the information transmission rate. This global optimum arises from a fundamental trade-off between the need to maximize the frequency of independent input messages, the necessity to respond fast to changes in the input, and the need to respond reliably to these changes. The optimal temperature lies above the critical point but moves toward it as the distance between the input and output spin is increased.
最近的实验表明，许多生物系统在其临界点附近会进行自组织，这暗示了一种共同的设计原则。虽然有人提出在临界点附近信息传输得到了优化，但信息传输如何依赖于输入信号的动态特性、信息需要传输的距离以及到临界点的距离仍不清楚。在这里，我们采用对受驱动的二维伊辛系统进行随机模拟的方法，研究了受驱动的输入自旋和输出自旋之间的瞬时互信息以及信息传输速率。瞬时互信息随温度呈非单调变化，但随输入信号的相关时间单调增加。相比之下，不仅存在一个最优温度，还存在一个最优的有限输入相关时间，可使信息传输速率最大化。这种全局最优源于在最大化独立输入消息频率的需求、对输入变化快速响应的必要性以及对这些变化可靠响应的需求之间的基本权衡。最优温度位于临界点之上，但随着输入和输出自旋之间的距离增加，它会向临界点移动。
