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

Journal Article · 05 January 2025 · Physical Review. E

DOI: https://doi.org/10.1103/physreve.111.014114 · OSTI ID:2496291

Klinger, Jérémie ^[1]; Rotskoff, Grant M.  ^[2]

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1. Stanford University, CA (United States); Stanford University
2. Stanford University, CA (United States)

The connection between measure theoretic optimal transport and dissipative nonequilibrium dynamics provides a language for quantifying nonequilibrium control costs, leading to a collection of thermodynamic speed limits, which rely on the assumption that the target probability distribution is perfectly realized. This is almost never the case in experiments or numerical simulations, so here we address the situation in which the external controller is imperfect. We obtain a lower bound for the dissipated work in generic nonequilibrium control problems that (1) is asymptotically tight and (2) matches the thermodynamic speed limit in the case of optimal driving. Along with analytically solvable examples, we refine this imperfect driving notion to systems in which the controlled degrees of freedom are slow relative to the nonequilibrium relaxation rate, and identify independent energy contributions from fast and slow degrees of freedom. Furthermore, we develop a strategy for optimizing minimally dissipative protocols based on optimal transport flow matching, a generative machine learning technique. Furthermore, this latter approach ensures the scalability of both the theoretical and computational framework we put forth. Crucially, we demonstrate that we can compute the terms in our bound numerically using efficient algorithms from the computational optimal transport literature and that the protocols we learn saturate the bound.

• Research Organization: Stanford University, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: SC0022917
• OSTI ID: 2496291
• Journal Information: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 1 Vol. 111; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English