Speed limit for open systems coupled to general environments

Abstract

In this study, we investigate the bound on the speed of state transformation in the quantum and classical systems that are coupled to general environment with arbitrary coupling interactions. We show that a Mandelstam-Tamm type speed limit exists and energy fluctuation still plays a crucial role in this speed limit inequality for open quantum systems. The energy fluctuation of the target system in addition to the coupling to the environment is key in the inequality. We also present the classical version of the speed limit for open systems. As potential applications of the proposed speed limit expression, we discuss the fundamental limitation of the state change in quantum cyclic engines and the equilibriation time required for the thermalization phenomena of isolated quantum systems.

10 pages, 1 figure

References in corpus (8)

• Thermalization and its mechanism for generic isolated quantum systems
• Driven quantum transport on the nanoscale
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Quantum speed limit for physical processes
• Quantum speed limits in open system dynamics
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Geometric derivation of the quantum speed limit
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving

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• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Active charge and discharge of a capacitor: scaling solution and energy optimization
• Optimal synchronisation to a limit cycle
• Quantum speed limits for an open system in contact with a thermal bath