This paper develops a theory establishing rigorous limits on the rate of fluctuation growth in non-equilibrium systems. It finds that an observable's fluctuation speed is upper-bounded by the fluctuation of a suitably chosen "velocity observable," revealing a tradeoff between mean and fluctuation changes. The theory's advantages are demonstrated in various contexts, including processes with significant observable dispersion, quantum work extraction, and entanglement growth in fermionic systems. The findings pave the way for a quantitative theory of fluctuation dynamics across diverse non-equilibrium systems.

Ryusuke Hamazaki