  The oscillation of fluctuation with two state observables is investigated.
Following the idea of Ohga, et al. [arXiv:2303.13116], we find that the
fluctuation oscillation relative to their autocorrelations is bounded from
above by the entropy production per characteristic maximum oscillation time.
Our result applies to a variety of systems including Langevin systems, chemical
reaction systems, and macroscopic systems. In addition, our bound consists of
experimentally tractable quantities, which enables us to examine our inequality
experimentally.
