Information-theoretical analysis of skyrmion dynamics at finite temperature in a box -- a simulation study

Tenta Tani, Soma Miki, Hiroki Mori, Minori Goto, Yoshishige Suzuki, Eiiti Tamura

Published 2024-12-25Version 1

We theoretically investigate the classical dynamics and 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. Through the analysis of information-theoretical quantities, we elucidate the physical significance of transfer entropy as a measure of information flow. 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.