  This study has applied information thermodynamics to a bivariate linear
stochastic differential equation (SDE) that describes a synchronization
phenomenon of sea surface temperatures (SSTs) between the Gulf Stream and the
Kuroshio Current, which is referred to as the boundary current synchronization
(BCS). Information thermodynamics divides the entire system fluctuating with
stochastic noise into subsystems and describes the interactions between these
subsystems from the perspective of information transfer. The SDE coefficients
have been estimated through regression analysis using observational and
numerical simulation data. In the absence of stochastic noise, the solution of
the estimated SDE shows that the SSTs relax toward zero without oscillating.
The estimated SDE can be interpreted as a Maxwell's demon system, with the Gulf
Stream playing the role of the "Particle" and the Kuroshio Current playing the
role of the "Demon." This interpretation gives the asymmetric roles of both
ocean currents. The Gulf Stream forces the SST of the Kuroshio Current to be in
phase. By contrast, the Kuroshio Current maintains the phase by interfering
with the relaxation of the Gulf Stream SST. In the framework of Maxwell's
demon, the Gulf Stream is interpreted as being measured by the Kuroshio
Current, whereas the Kuroshio Current is interpreted as performing feedback
control on the Gulf Stream. When the Gulf Stream and the Kuroshio Current are
coupled in an appropriate parameter regime, synchronization is realized with
atmospheric and oceanic noise as the driving source.
