The oscillation of fluctuation with two state observables is investigated. Following the idea of Ohga et al. [Phys. Rev. Lett. 131, 077101 (2023)], 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.

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• Stochastic processes
• Stochastic thermodynamics
• Nonequilibrium systems
• Chemical waves