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. By numerical simulations based on the Thiele-Langevin equation, we demonstrate that the skyrmion motion cannot be fully described by the master equation, highlighting the nontrivial dynamics. Particularly, due to the chiral motion of skyrmion, we find asymmetric flow of information with violating the detailed balance condition. We analyze this system using information-theoretical quantities including Shannon entropy, mutual information, and transfer entropy. The physical significance of transfer entropy, which has been overlooked in previous studies, is elucidated. Notably, the peak position of the transfer entropy, as a function of time delay, is independent of the interaction range yet dependent on the box size. This peak corresponds to the characteristic time required for changing the skyrmion state. Due to the unusual asymmetric circulation of information, the two-skyrmion system can be a unique device for future applications to the natural computing.