Transfer entropy and flow of information in two-skyrmion system

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.
Comment: 13 pages, 8 figures