Universal energy-speed-accuracy trade-offs in driven nonequilibrium systems

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Machine Learning
• Optimal Transport Theory

Background:

• Measure theoretic optimal transport offers a framework for quantifying nonequilibrium control costs and establishing thermodynamic speed limits.
• Existing speed limits assume perfect realization of target distributions, which is often unachievable in practical experiments and simulations.
• Imperfect control introduces challenges in accurately assessing and minimizing thermodynamic costs.

Purpose of the Study:

• To derive a lower bound for dissipated work in generic nonequilibrium control problems with imperfect external controllers.
• To analyze the behavior of this bound in systems with varying relaxation rates and identify energy contributions from different degrees of freedom.
• To develop a scalable strategy for optimizing minimally dissipative protocols using generative machine learning.

Main Methods:

• Developed a novel lower bound for dissipated work applicable to imperfect nonequilibrium control.
• Analyzed imperfect driving in systems with slow controlled degrees of freedom relative to relaxation rates.
• Employed optimal transport flow matching, a generative machine learning technique, for protocol optimization.

Main Results:

• Derived an asymptotically tight lower bound for dissipated work in imperfect control scenarios.
• The bound converges to the thermodynamic speed limit under optimal driving conditions.
• Identified independent energy contributions from fast and slow degrees of freedom in specific systems.
• Demonstrated numerical computation of bound terms using computational optimal transport algorithms.
• Developed machine learning-derived protocols that saturate the derived bound.

Conclusions:

• The derived lower bound provides a robust measure of thermodynamic cost under realistic, imperfect control conditions.
• The optimal transport flow matching approach offers a scalable and computationally efficient method for designing minimally dissipative protocols.
• This work bridges theoretical thermodynamics with practical control strategies, enhanced by machine learning.