Optimal Control of Periodic Nonequilibrium Mechanochemical Systems via Automatic Differentiation
Abstract
Biological molecular machines are mesoscopic systems that act repeatedly and periodically to perform important cellular tasks while contending with strong fluctuations and operating in an overdamped regime. Optimal control theory is a tool that can be used to understand the design principles behind efficient operation of these machines; however, most studies on optimal control of classical mesoscopic systems have focused on control problems that do not repeat periodically. Here, we automatically differentiate Fokker-Planck simulations to design efficient nonequilibrium control strategies for simple models of periodic molecular machines with and without explicit changes in the machine's chemical state. The designed protocols and theoretical analysis provide insight into the design principles governing efficient driving in these nonequilibrium systems. Designed control protocols should seek to reduce mechanical heat by rotating the entire angular probability distribution at a constant speed without changing its shape, and should reduce chemical heat by reducing the proportion of chemical transitions with large heat.
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BibTeX
@misc{wareham2026optimal,
title = {{Optimal Control of Periodic Nonequilibrium Mechanochemical Systems via Automatic Differentiation}},
author = {W. Callum Wareham and David A. Sivak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03217},
eprint = {2609.03217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03217},
}
RIS
TY - UNPB
TI - Optimal Control of Periodic Nonequilibrium Mechanochemical Systems via Automatic Differentiation
AU - W. Callum Wareham
AU - David A. Sivak
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.03217
UR - https://arxiv.org/abs/2609.03217
AB - Biological molecular machines are mesoscopic systems that act repeatedly and periodically to perform important cellular tasks while contending with strong fluctuations and operating in an overdamped regime. Optimal control theory is a tool that can be used to understand the design principles behind efficient operation of these machines; however, most studies on optimal control of classical mesoscopic systems have focused on control problems that do not repeat periodically. Here, we automatically differentiate Fokker-Planck simulations to design efficient nonequilibrium control strategies for simple models of periodic molecular machines with and without explicit changes in the machine's chemical state. The designed protocols and theoretical analysis provide insight into the design principles governing efficient driving in these nonequilibrium systems. Designed control protocols should seek to reduce mechanical heat by rotating the entire angular probability distribution at a constant speed without changing its shape, and should reduce chemical heat by reducing the proportion of chemical transitions with large heat.
ER -