标题： 转移熵和双磁子系统中的信息流 显示英文标题

标题： Transfer entropy and flow of information in two-skyrmion system

摘要： 我们理论研究了在有限温度下被限制在一个盒子中的相互作用的两个skyrmion系统中的信息流动。 使用基于Thiele-Langevin方程的数值模拟，我们证明skyrmion运动不能完全由主方程描述，突显了该系统的简单性及其非平凡的动力学特性。 特别是，由于skyrmion的螺旋运动，即使在平衡状态下我们也发现信息流动的不对称性，这通过详细平衡条件的破坏得到证实。 我们利用包括香农熵、互信息和转移熵在内的信息理论量来分析这个新奇的系统。 通过这些分析，阐明了转移熵作为信息流动度量的物理意义，这一意义在以前的研究中被忽视了。 值得注意的是，作为时间延迟函数的转移熵的峰值位置似乎与两个skyrmion之间的相互作用范围无关，但与盒子大小有关。 这个峰值对应于改变skyrmion状态所需的时间：盒子大小除以skyrmion的平均速度。 我们可以理解信息传输时间包括获取互信息的时间和写入信息的时间。 由于在这个两skyrmion系统中揭示了不寻常的信息不对称循环，它可能成为未来利用信息流动进行自然计算的独特平台，包括更高效机器学习算法的应用。 显示英文摘要

摘要： We theoretically investigate the flow of information in an interacting two-skyrmion system confined in a box at finite temperature. Using numerical simulations based on the Thiele-Langevin equation, we demonstrate that the skyrmion motion cannot be fully described by the master equation, highlighting the system's simplicity with its nontrivial dynamics. Particularly, due to the chiral motion of skyrmion, we find asymmetric flow of information even in equilibrium, which is demonstrated by the violation of the detailed balance condition. We analyze this novel system using information-theoretical quantities including Shannon entropy, mutual information, and transfer entropy. By the analyses, the physical significance of transfer entropy as a measure of flow of information, which has been overlooked in previous studies, is elucidated. Notably, the peak position of the transfer entropy, as a function of time delay, is found to be independent of the interaction range between the two skyrmions yet dependent on the box size. This peak corresponds to the characteristic time required for changing the skyrmion state: the box size divided by the average velocity of skyrmions. We can understand that the information transmission time consists of the time to obtain mutual information and the time to write the information. Since the unusual asymmetric circulation of information is revealed in this two-skyrmion system, it can be a unique platform for future applications to natural computing using flow of information, including more efficient machine learning algorithm.