Abstract
Information-to-energy conversion with feedback measurement stands as one of the most intriguing aspects of the thermodynamics of information in the nanoscale. To date, experiments have focused on feedback protocols for work extraction. Here we address the novel case of dissipation reduction in nonequilibrium systems with feedback. We perform pulling experiments on DNA hairpins with optical tweezers, with a general feedback protocol based on multiple measurements that includes either discrete-time or continuous-time feedback. While feedback can reduce dissipation, it remains unanswered whether it also improves free-energy determination (information-to-measurement conversion). We define thermodynamic information as the natural logarithm of the feedback efficacy, a quantitative measure of the efficiency of information-to-energy and information-to-measurement conversion in feedback protocols. We find that discrete- and continuous-time feedback reduces dissipation by roughly without improvement in free-energy determination. Remarkably, a feedback strategy (defined as a correlated sequence of feedback protocols) further reduces dissipation, enhancing information-to-measurement efficiency. Our study underlines the role of temporal correlations to develop feedback strategies for efficient information-to-measurement conversion in small systems.
- Received 6 November 2020
- Revised 17 June 2021
- Accepted 30 June 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031052
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
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Popular Summary
Thermodynamics of small systems under feedback control has emerged as a fertile field of research in physics and beyond. In particular, information-to-energy conversion in feedback systems has become a major quest in theory and experiment. To date, feedback protocols have focused on work extraction in equilibrium systems such as colloidal systems, electrical devices, or single molecules. However, most systems in nature are out of equilibrium and dissipative. Can we use feedback to reduce dissipation in nonequilibrium systems? Can we take advantage of such a reduction to extract equilibrium information (e.g., a system’s free energy)? Here, we combine theory and experiment to investigate how feedback reduces dissipation in small nonequilibrium systems.
As a model out-of-equilibrium system, we take DNA “hairpins”—short stem-loop structures that fold back on themselves—and gently pull on their ends to straighten the hairpins out, all the while measuring the applied force on the DNA. We use these data to introduce and demonstrate a novel and general single-decision feedback protocol to reduce dissipation when pulling. Key to our study is “thermodynamic information,” a novel energy term that quantifies the reduction in dissipation (information-to-energy conversion) and the improvement in free-energy determination (information-to-measurement conversion).
While single-decision feedback reduces dissipation, we observe that it cannot be used to weaken the second law of thermodynamics inequality any further, showing that information-to-measurement conversion is much less efficient than information-to-energy conversion. In contrast, a combination of correlated decision protocols (a strategy) performs much better. Our study shows the crucial role of strategies for efficient information-to-measurement conversion in small systems.
