- Access by Xinjiang University
Strong violation of the thermodynamic uncertainty relation in a minimal autonomous heat engine
Phys. Rev. E 114, 024153 – Published 25 August, 2026
DOI: https://doi.org/10.1103/2tdv-rjq5
Abstract
Thermodynamic uncertainty relations (TURs) impose a universal trade-off between current precision and entropy production in autonomous steady states, constraining in particular the power, efficiency, and constancy of heat engines. We demonstrate strong violations of the long-time TUR in a minimal autonomous heat engine composed of a discrete ratchet generating work against a constant bias and an underdamped harmonic oscillator acting as an internal stochastic control. In the regime of timescale separation, the model becomes exactly solvable and yields a closed analytical expression for the TUR ratio, where the influence of the continuous degree of freedom is fully captured by the Fano factor of oscillator zero crossings. We show that increasingly deterministic internal control drives the TUR ratio arbitrarily close to zero while the engine operates near maximal current and efficiency. In an appropriate limit, the model reduces to the classical pendulum-clock system of Pietzonka [Phys. Rev. Lett. 128, 130606 (2022)].
Physics Subject Headings (PhySH)
Article Text
References (29)
- V. Holubec and A. Ryabov, Fluctuations in heat engines, J. Phys. A: Math. Theor. 55, 013001 (2022).
- J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine, Science 352, 325 (2016).
- I. A. Martínez, E. Roldán, L. Dinis, and R. A. Rica, Colloidal heat engines: A review, Soft Matter 13, 22 (2017).
- I. A. Martínez, E. Roldán, L. Dinis, D. Petrov, and R. A. Rica, Adiabatic processes realized with a trapped Brownian particle, Phys. Rev. Lett. 114, 120601 (2015).
- S. Ciliberto, Experiments in stochastic thermodynamics: Short history and perspectives, Phys. Rev. X 7, 021051 (2017).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
- A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
- T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Dissipation bounds all steady-state current fluctuations, Phys. Rev. Lett. 116, 120601 (2016).
- J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020).
- P. Pietzonka and U. Seifert, Universal trade-off between power, efficiency, and constancy in steady-state heat engines, Phys. Rev. Lett. 120, 190602 (2018).
- H.-M. Chun, L. P. Fischer, and U. Seifert, Effect of a magnetic field on the thermodynamic uncertainty relation, Phys. Rev. E 99, 042128 (2019).
- P. Pietzonka, Classical pendulum clocks break the thermodynamic uncertainty relation, Phys. Rev. Lett. 128, 130606 (2022).
- Y. Hasegawa, Thermodynamic uncertainty relation for general open quantum systems, Phys. Rev. Lett. 126, 010602 (2021).
- V. Holubec and A. Ryabov, Cycling tames power fluctuations near optimum efficiency, Phys. Rev. Lett. 121, 120601 (2018).
- L. Razzoli, M. Carrega, F. Cavaliere, G. Benenti, and M. Sassetti, Synchronization-induced violation of thermodynamic uncertainty relations, Quantum Sci. Technol. 9, 045032 (2024).
- L. Razzoli, F. Cavaliere, M. Carrega, M. Sassetti, and G. Benenti, Efficiency and thermodynamic uncertainty relations of a dynamical quantum heat engine, Eur. Phys. J.: Spec. Top. 233, 1263 (2024).
- J. S. Lee, J.-M. Park, and H. Park, Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force, Phys. Rev. E 100, 062132 (2019).
- R.-S. Fu and T. R. Gingrich, Thermodynamic uncertainty relation for Langevin dynamics by scaling time, Phys. Rev. E 106, 024128 (2022).
- K. Ptaszyński, Coherence-enhanced constancy of a quantum thermoelectric generator, Phys. Rev. B 98, 085425 (2018).
- B. K. Agarwalla and D. Segal, Assessing the validity of the thermodynamic uncertainty relation in quantum systems, Phys. Rev. B 98, 155438 (2018).
- T. Ehrlich and G. Schaller, Broadband frequency filters with quantum dot chains, Phys. Rev. B 104, 045424 (2021).
- A. A. S. Kalaee, A. Wacker, and P. P. Potts, Violating the thermodynamic uncertainty relation in the three-level maser, Phys. Rev. E 104, L012103 (2021).
- A. M. Timpanaro, G. Guarnieri, and G. T. Landi, Quantum thermoelectric transmission functions with minimal current fluctuations, Phys. Rev. B 111, 014301 (2025).
- F. Meier, Y. Minoguchi, S. Sundelin, T. J. G. Apollaro, P. Erker, S. Gasparinetti, and M. Huber, Precision is not limited by the second law of thermodynamics, Nat. Phys. 21, 1147 (2025).
- L. P. Fischer, H.-M. Chun, and U. Seifert, Free diffusion bounds the precision of currents in underdamped dynamics, Phys. Rev. E 102, 012120 (2020).
- E. P. Cital and V. Holubec, Inertia tames fluctuations in autonomous stationary heat engines, New J. Phys. 28, 034605 (2026).
- A. C. Barato and U. Seifert, Cost and precision of Brownian clocks, Phys. Rev. X 6, 041053 (2016).
- P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Autonomous quantum clocks: Does thermodynamics limit our ability to measure time? Phys. Rev. X 7, 031022 (2017).
- H. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
