Topological Speed Limit

Abstract

Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

arXiv comment7+11 pages, 2+2 figures

References in corpus (64)

• Quantum metrology
• Quantum Communication Through an Unmodulated Spin Chain
• Ultimate physical limits to computation
• The ITensor Software Library for Tensor Network Calculations
• The maximum speed of dynamical evolution
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Optimal Control at the Quantum Speed Limit
• Quantum speed limits in open system dynamics
• Irreversible entropy production, from quantum to classical
• Generalized Geometric Quantum Speed Limits
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• Speed Limit for Classical Stochastic Processes
• Trade-off between speed and cost in shortcuts to adiabaticity
• Optimal protocols and optimal transport in stochastic thermodynamics
• Generalized Wasserstein distance and its application to transport equations with source
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Breakdown of quasilocality in long-range quantum lattice models
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Quantum Speed Limit is Not Quantum
• Finite-time Landauer principle
• Tightening Quantum Speed Limits for Almost All States
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Quantum thermodynamic uncertainty relation for continuous measurement
• Stochastic thermodynamic interpretation of information geometry
• Speed limit for open quantum systems
• Time-information uncertainty relations in thermodynamics
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Communication at the quantum speed limit along a spin chain
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Nonlinear quantum metrology of many-body open systems
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Geometric Speed Limit of Accessible Many-Body State Preparation
• The Lieb-Robinson light cone for power-law interactions
• Tight, robust, and feasible quantum speed limits for open dynamics
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Finite-Time Quantum Landauer Principle and Quantum Coherence
• Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
• Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
• Geometric quantum speed limits: a case for Wigner phase space
• Optimal control of a qubit in an optical cavity
• Action quantum speed limits
• Universal Bound on Energy Cost of Bit Reset in Finite Time
• Probing Quantum Speed Limits with Ultracold Gases
• Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks
• Energetic cost of Hamiltonian quantum gates
• Speed Limits for Macroscopic Transitions
• Speed limit for a highly irreversible process and tight finite-time Landauer's bound
• Quantum Speed Limits under Continuous Quantum Measurements
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• On Lieb-Robinson bounds for the Bose-Hubbard model
• Finite speed of quantum information in models of interacting bosons at finite density
• Quantum speed limit for thermal states
• Measurement induced quantum walks
• Speed limits of the trace distance for open quantum system
• Speed limit for open systems coupled to general environments
• Lower bound for entropy production rate in stochastic systems far from equilibrium
• A Class of Time-Energy Uncertainty Relations for Time-dependent Hamiltonians
• Classical and quantum speed limits

Cited by in corpus (28)

• Optimal Control in Stochastic Thermodynamics
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Geometric thermodynamics for the Fokker-Planck equation: Stochastic thermodynamic links between information geometry and optimal transport
• Thermomajorization Mpemba Effect
• Quantum Speed Limit under Brachistochrone Evolution
• Quantum speed limits in arbitrary phase spaces
• Fundamental speed limits on entanglement dynamics of bipartite quantum systems
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Fidelity-dissipation relations in quantum gates
• Inferring kinetics and entropy production from observable transitions in partially accessible, periodically driven Markov networks
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• Geometric characterization for cyclic heat engines far from equilibrium
• Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
• Infinite variety of thermodynamic speed limits with general activities
• Speed limits to fluctuation dynamics
• Role of interactions in non-equilibrium transformations
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Quantum speed limit for the OTOC from an open systems perspective
• Wasserstein distance in speed limit inequalities for Markov jump processes
• Information geometric bound on general chemical reaction networks
• Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems
• Fractionally Quantized Recurrence Detection Times in Monitored Quantum Many-Body Systems
• Effect of measurements on quantum speed limit
• Implementation of multiparticle quantum speed limits on observables
• Universal trade-off between irreversibility and intrinsic timescale in thermal relaxation with applications to thermodynamic inference
• Critical Scaling of the Quantum Wasserstein Distance
• Time-cost-error trade-off relation in thermodynamics: The third law and beyond