Speed limits to fluctuation dynamics

TL;DR

This paper establishes rigorous speed limits for the growth of fluctuations in nonequilibrium systems, revealing fundamental constraints and tradeoffs between mean and fluctuation dynamics across quantum and classical systems.

Contribution

It introduces a novel theoretical framework that bounds the rate of fluctuation growth, extending the understanding of dynamical constraints beyond mean behavior.

Findings

Derived universal bounds on fluctuation growth rates.

Demonstrated inequalities' advantages in quantum work extraction.

Applied results to entanglement growth in fermionic systems.

Abstract

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics.