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Topological Speed Limit.

Tan Van Vu1, Keiji Saito1

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|January 20, 2023
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Summary
This summary is machine-generated.

Scientists developed a unified topological speed limit for physical systems. This limit, based on optimal transport and discrete Wasserstein distance, constrains how fast states can change, applicable from classical to quantum dynamics.

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Area of Science:

  • Theoretical Physics
  • Physical Chemistry
  • Quantum Dynamics

Background:

  • Physical systems evolve at finite speeds, limited by energy costs and the topology of their dynamics.
  • Understanding these constraints is crucial for optimizing system evolution and designing faster processes.

Purpose of the Study:

  • To derive a unified topological speed limit for physical state evolution.
  • To incorporate topological information into speed limit calculations.
  • To provide insights into achieving maximum process speed.

Main Methods:

  • Optimal transport approach to derive the speed limit.
  • Utilizing discrete Wasserstein distance to encode topological information.
  • Analyzing time-averaged velocity in conjunction with topological constraints.

Main Results:

  • A unified topological speed limit for physical systems was derived.
  • The minimum time for state change is lower bounded by discrete Wasserstein distance and time-averaged velocity.
  • The derived bound is tight and applicable to diverse systems (deterministic, stochastic, classical, quantum).

Conclusions:

  • The topological speed limit offers a universal framework for understanding evolution constraints.
  • The findings provide design principles for optimizing the speed of physical processes.
  • Applications demonstrated in chemical reaction networks and quantum many-body systems.