Entropy production limits all fluctuation oscillations

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.