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Non-equilibrium entropy production and information dissipation in a non-Markovian quantum dot

Nature Physics volume 22, pages 374–381 (2026)Cite this article

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Abstract

The work required to drive a system from one state to another comprises both the equilibrium free energy difference and the dissipation associated with irreversibility. As physical processes—such as computing—approach fast limits, calculating this excess dissipation becomes increasingly critical. Yet, precisely quantifying dissipation, more specifically, entropy production, in strongly driven, time-dependent, realistic nanoscale systems remains a considerable challenge. Consequently, previous studies have largely been limited to either idealized Markovian systems under time-dependent driving or non-Markovian steady-state systems under constant driving. Here we measure the full dynamics of trajectory-level entropy production in a non-stationary, non-Markovian material arising from time-dependent driving. We use machine learning to extract the entropy produced by a quantum dot stochastically blinking under a stepwise control protocol. The entropy produced corresponds to the loss of memory in the material as the carrier distribution evolves. In addition, our approach quantifies both information insertion and dissipation under a quenched protocol. This work demonstrates a simple and effective approach for visualizing dissipation dynamics following a fast quench and serves as a stepping stone towards optimizing energy costs in the control of real materials and devices.

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Fig. 1: Experimental scheme, carrier dynamics and entropy production in non-equilibrium QD blinking.
Fig. 2: QD blinking statistics with NIR laser field off and on.
Fig. 3: Enabled by machine learning, a HMM interprets and reproduces the experimental results.
Fig. 4: Dynamics of trajectory-level entropy production.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request.

Code availability

The codes used in this work are available publicly at http://codeocean.com/signup/nature?token=0bf0606b4f9e4cd59b0ed7b9efcc731d.

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Acknowledgements

This work was supported primarily by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (Contract No. DE-AC02-76SF00515). F.L. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences, CPIMS Program (Award No. DE-SC0026181). We thank P. H. Bucksbaum for generously providing access to his laboratory and the laser facilities used in this work. We are grateful to H. Qin and X. Peng for supplying the QD samples and to Z. Jiang (Karunadasa Group) for providing the PMMA for sample preparation. We also acknowledge valuable discussions with Y. Huang, Y. Jiang and Y. Du regarding the QD identification algorithm and machine learning approaches.

Author information

Author notes

  1. These authors contributed equally: Yuejun Shen, Chutian Chen.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    Yuejun Shen, Jiaojian Shi & Aaron M. Lindenberg

  2. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Yuejun Shen, Jiaojian Shi & Aaron M. Lindenberg

  3. Institute of Physics, University of Amsterdam, Amsterdam, The Netherlands

    Chutian Chen

  4. Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Haoran Ma, Christian Heide & Aaron M. Lindenberg

  5. Department of Physics, Stanford University, Stanford, CA, USA

    Haoran Ma

  6. Department of Chemistry, Stanford University, Stanford, CA, USA

    Ashley P. Saunders, Fang Liu & Grant M. Rotskoff

  7. Department of Physics, University of Central Florida, Orlando, FL, USA

    Christian Heide

  8. CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

    Christian Heide

  9. Department of Chemistry, University of Washington, Seattle, WA, USA

    Jiaojian Shi

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Contributions

Y.S., J.S. and A.M.L. conceived the project and initiated the experimental effort. C.C., Y.S. and G.M.R. developed the theoretical framework and constructed the model. Y.S. and H.M. performed the data acquisition. Y.S., A.P.S. and F.L. were responsible for sample preparation. C.H. optimized the laser system. Y.S. and C.C. led the writing of the paper. A.M.L. supervised the project.

Corresponding author

Correspondence to Aaron M. Lindenberg.

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Nature Physics thanks Paul Eastham, Richard Geilhufe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The workflow of optimizing the parameters for the HMM.

Experimental data are split into train and test sets. Model parameters are optimized by minimizing the loss (top left) on the train data and validated by comparing losses on train and test sets. Bottom left: field-off parameters are optimized first and used for subsequent field-on optimization.

Supplementary information

Supplementary Information (download PDF )

Supplementary Notes 1–7, Figs. 1–12 and Table 1.

Supplementary Video 1 (download MP4 )

A viscous system under pulsed excitations.

Supplementary Video 2 (download AVI )

PL measurement of QD blinking under a periodically applied NIR field.

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Shen, Y., Chen, C., Ma, H. et al. Non-equilibrium entropy production and information dissipation in a non-Markovian quantum dot. Nat. Phys. 22, 374–381 (2026). https://doi.org/10.1038/s41567-026-03177-8

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