Speed Limits for Macroscopic Transitions

Abstract

Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive studies have made efforts to obtain rigorous constraints on dynamical processes since Mandelstam and Tamm, speed limits that provide tight bounds for macroscopic transitions have remained elusive. Here, by employing the local conservation law of probability, the fundamental principle in physics, we develop a general framework for deriving qualitatively tighter speed limits for macroscopic systems than many conventional ones. We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph, which can describe general many-body systems, is bounded by the "gradient" of the observable, in contrast with conventional speed limits depending on the entire range of the observable. This framework enables us to derive novel quantum speed limits for macroscopic unitary dynamics. Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases; this intuitively describes a new tradeoff relation between time and quantum phase difference. Our bound is dependent on instantaneous quantum states and thus can achieve the equality condition, which is conceptually distinct from the Lieb-Robinson bound. Our work elucidates novel speed limits on the basis of local conservation law, providing fundamental limits to various types of nonequilibrium quantum macroscopic phenomena.

36 pages, 13 figures

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• Bounds in Nonequilibrium Quantum Dynamics
• Quantum Speed Limits for Observables
• Quantum speed limits on operator flows and correlation functions
• Topological Speed Limit
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Thermodynamic speed limits for mechanical work
• Observational entropy, coarse quantum states, and Petz recovery: information-theoretic properties and bounds
• Thermodynamic correlation inequality
• Unified entropies and quantum speed limits for nonunitary dynamics
• Quantum speed limits in arbitrary phase spaces
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices