Speed limit for open systems coupled to general environments

We investigate the bound on the speed of state transformation in the quantum systems that are coupled to general environments. We focus on the energy fluctuation of the target system and the coupling to the environment, and clarify the universal constraint on the state transformation deriving the general speed-limit inequality. This speed-limit inequality is applicable to any open systems including physical situations that have not been studied so far. We apply the inequality to the thermalization phenomena in isolated quantum systems, and the quantum cyclic engines. For the thermalization, we provide several inequalities to estimate the equilibration time. In the cyclic heat engines, we derive a rigorous constraint on the state change in the cycle where the Planck constant plays a fundamental role.

Automated summary

This study investigates the speed limit on state transformation in quantum systems coupled to general environments, deriving a general speed-limit inequality applicable to various open systems. The inequality is applied to thermalization phenomena in isolated quantum systems and quantum cyclic engines, providing multiple inequalities to estimate equilibration time. Additionally, a rigorous constraint on state change in cyclic heat engines is derived, with Planck constant playing a fundamental role in the cycle.