- Open Access
Precision of an autonomous demon exploiting nonthermal resources and information
Phys. Rev. B 113, 195442 – Published 27 May, 2026
DOI: https://doi.org/10.1103/hnqk-6rcx
Abstract
Quantum-dot systems serve as nanoscale heat engines exploiting thermal fluctuations to perform a useful task. Here we investigate a multiterminal triple-dot system, operating as a refrigerator that extracts heat from a cold electronic contact. In contrast to standard heat engines, this system exploits a nonthermal resource. This has the intriguing consequence that cooling can occur without extracting energy from the resource on average—a seemingly demonic action—while, however, requiring the resource to fluctuate. Using full counting statistics and stochastic trajectories, we analyze the performance of the device in terms of the cooling-power precision, employing performance quantifiers motivated by the thermodynamic and kinetic uncertainty relations. We focus on two regimes with large output power, which are based on two operational principles: exploiting information on one hand and the nonthermal properties of the resource on the other. We show that these regimes significantly differ in precision. In particular, the regime exploiting the nonthermal properties of the resource can have cooling-power fluctuations that are suppressed with respect to the input fluctuations by an order of magnitude. We also substantiate the interpretation of the two different working principles by analyzing cross-correlations between input and output heat currents and information flow.
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References (89)
- Edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime (Springer International Publishing, Cham, Switzerland, 2018).
- S. Campbell, I. D'Amico, M. A. Ciampini, J. Anders, N. Ares, S. Artini, A. Auffèves, L. B. Oftelie, L. P. Bettmann, M. V. S. Bonança, T. Busch, M. Campisi, M. F. Cavalcante, L. A. Correa, E. Cuestas, C. B. Dag, S. Dago, S. Deffner, A. Del Campo, A. Deutschmann-Olek, et al., Roadmap on quantum thermodynamics, Quantum Sci. Technol. 11, 012501 (2026).
- G. Benenti, G. Casati, K. Saito, and R. S. Whitney, Fundamental aspects of steady-state conversion of heat to work at the nanoscale, Phys. Rep. 694, 1 (2017).
- A. A. M. Staring, L. W. Molenkamp, B. W. Alphenaar, H. van Houten, O. J. A. Buyk, M. A. A. Mabesoone, C. W. J. Beenakker, and C. T. Foxon, Coulomb-blockade oscillations in the thermopower of a quantum dot, Europhys. Lett. 22, 57 (1993).
- A. S. Dzurak, C. G. Smith, M. Pepper, D. A. Ritchie, J. E. F. Frost, G. A. C. Jones, and D. G. Hasko, Observation of Coulomb blockade oscillations in the thermopower of a quantum dot, Solid State Commun. 87, 1145 (1993).
- R. Scheibner, E. G. Novik, T. Borzenko, M. König, D. Reuter, A. D. Wieck, H. Buhmann, and L. W. Molenkamp, Sequential and cotunneling behavior in the temperature-dependent thermopower of few-electron quantum dots, Phys. Rev. B 75, 041301(R) (2007).
- S. F. Svensson, A. I. Persson, E. A. Hoffmann, N. Nakpathomkun, H. A. Nilsson, H. Q. Xu, L. Samuelson, and H. Linke, Lineshape of the thermopower of quantum dots, New J. Phys. 14, 033041 (2012).
- M. Josefsson, A. Svilans, A. M. Burke, E. A. Hoffmann, S. Fahlvik, C. Thelander, M. Leijnse, and H. Linke, A quantum-dot heat engine operating close to the thermodynamic efficiency limits, Nat. Nanotechnol. 13, 920 (2018).
- D. Prete, P. A. Erdman, V. Demontis, V. Zannier, D. Ercolani, L. Sorba, F. Beltram, F. Rossella, F. Taddei, and S. Roddaro, Thermoelectric conversion at 30 K in InAs/InP nanowire quantum dots, Nano Lett. 19, 3033 (2019).
- S. Volosheniuk, R. Conte, E. Pyurbeeva, T. Baum, M. Vilas-Varela, S. Fernández, D. Peña, H. S. J. van der Zant, and P. Gehring, A single-molecule quantum heat engine, Nano Lett. 26, 984 (2026).
- B. Roche, P. Roulleau, T. Jullien, Y. Jompol, I. Farrer, D. A. Ritchie, and D. C. Glattli, Harvesting dissipated energy with a mesoscopic ratchet, Nat. Commun. 6, 6738 (2015).
- F. Hartmann, P. Pfeffer, S. Höfling, M. Kamp, and L. Worschech, Voltage fluctuation to current converter with Coulomb-coupled quantum dots, Phys. Rev. Lett. 114, 146805 (2015).
- H. Thierschmann, R. Sánchez, B. Sothmann, F. Arnold, C. Heyn, W. Hansen, H. Buhmann, and L. W. Molenkamp, Three-terminal energy harvester with coupled quantum dots, Nat. Nanotechnol. 10, 854 (2015).
- S. Dorsch, A. Svilans, M. Josefsson, B. Goldozian, M. Kumar, C. Thelander, A. Wacker, and A. Burke, Heat driven transport in serial double quantum dot devices, Nano Lett. 21, 988 (2021).
- S. Dorsch, S. Fahlvik, and A. Burke, Characterization of electrostatically defined bottom-heated InAs nanowire quantum dot systems, New J. Phys. 23, 125007 (2021).
- S. Haldar, D. Zenelaj, P. P. Potts, H. Havir, S. Lehmann, K. A. Dick, P. Samuelsson, and V. F. Maisi, Microwave power harvesting using resonator-coupled double quantum dot photodiode, Phys. Rev. B 109, L081403 (2024).
- J. V. Koski, V. F. Maisi, T. Sagawa, and J. P. Pekola, Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon, Phys. Rev. Lett. 113, 030601 (2014).
- J. V. Koski, A. Kutvonen, I. M. Khaymovich, T. Ala-Nissila, and J. P. Pekola, On-chip Maxwell's demon as an information-powered refrigerator, Phys. Rev. Lett. 115, 260602 (2015).
- K. Chida, S. Desai, K. Nishiguchi, and A. Fujiwara, Power generator driven by Maxwell's demon, Nat. Commun. 8, 15301 (2017).
- R. S. Whitney, Illusory cracks in the second law of thermodynamics in quantum nanoelectronics, arXiv:2304.03106.
- A. de Oliveira Junior, J. B. Brask, and R. Chaves, A friendly guide to exorcising Maxwell's demon, PRX Quantum 6, 030201 (2025).
- R. Sánchez, J. Splettstoesser, and R. S. Whitney, Nonequilibrium system as a demon, Phys. Rev. Lett. 123, 216801 (2019).
- S. Ciliberto, Autonomous out-of-equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations, Phys. Rev. E 102, 050103(R) (2020).
- S. E. Deghi and R. A. Bustos-Marún, Entropy current and efficiency of quantum machines driven by nonequilibrium incoherent reservoirs, Phys. Rev. B 102, 045415 (2020).
- F. Hajiloo, R. Sánchez, R. S. Whitney, and J. Splettstoesser, Quantifying nonequilibrium thermodynamic operations in a multiterminal mesoscopic system, Phys. Rev. B 102, 155405 (2020).
- J. Lu, J.-H. Jiang, and Y. Imry, Unconventional four-terminal thermoelectric transport due to inelastic transport: Cooling by transverse heat current, transverse thermoelectric effect, and Maxwell demon, Phys. Rev. B 103, 085429 (2021).
- H. Yamazaki, M. Uemura, H. Tanaka, T. Hata, C. Lin, T. Akiho, K. Muraki, and T. Fujisawa, Efficient heat-energy conversion from a non-thermal Tomonaga-Luttinger liquid, Commun. Phys. 8, 387 (2025).
- R. S. Whitney, R. Sánchez, F. Haupt, and J. Splettstoesser, Thermoelectricity without absorbing energy from the heat sources, Physica E 75, 257 (2016).
- R. Sánchez, P. Samuelsson, and P. P. Potts, Autonomous conversion of information to work in quantum dots, Phys. Rev. Res. 1, 033066 (2019).
- Q. Cao and J. He, A four-terminal thermoelectric heat engine based on three coupled quantum dots, Eur. Phys. J. B 98, 136 (2025).
- J. Monsel, M. Acciai, R. Sánchez, and J. Splettstoesser, Autonomous demon exploiting heat and information at the trajectory level, Phys. Rev. B 111, 045419 (2025).
- M. Acciai, L. Tesser, J. Eriksson, R. Sánchez, R. S. Whitney, and J. Splettstoesser, Constraints between entropy production and its fluctuations in nonthermal engines, Phys. Rev. B 109, 075405 (2024).
- G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics, PRX Quantum 5, 020201 (2024).
- A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
- I. Di Terlizzi and M. Baiesi, Kinetic uncertainty relation, J. Phys. A: Math. Theor. 52, 02LT03 (2019).
- K. Brandner, T. Hanazato, and K. Saito, Thermodynamic bounds on precision in ballistic multiterminal transport, Phys. Rev. Lett. 120, 090601 (2018).
- V. T. Vo, T. Van Vu, and Y. Hasegawa, Unified thermodynamic–kinetic uncertainty relation, J. Phys. A: Math. Theor. 55, 405004 (2022).
- K. Brandner and K. Saito, Thermodynamic uncertainty relations for coherent transport, Phys. Rev. Lett. 135, 046302 (2025).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/hnqk-6rcx for additional plots covering alternative observables and further parameter regimes.
- W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven, Electron transport through double quantum dots, Rev. Mod. Phys. 75, 1 (2002).
- R. Sánchez and M. Büttiker, Optimal energy quanta to current conversion, Phys. Rev. B 83, 085428 (2011).
- A. Levy and R. Kosloff, Quantum absorption refrigerator, Phys. Rev. Lett. 108, 070604 (2012).
- D. Venturelli, R. Fazio, and V. Giovannetti, Minimal self-contained quantum refrigeration machine based on four quantum dots, Phys. Rev. Lett. 110, 256801 (2013).
- P. A. Erdman, B. Bhandari, R. Fazio, J. P. Pekola, and F. Taddei, Absorption refrigerators based on Coulomb-coupled single-electron systems, Phys. Rev. B 98, 045433 (2018).
- I. A. Picatoste and R. Sánchez, All-thermal reversal of heat currents using qutrits, Phys. Rev. A 110, 022210 (2024).
- P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Thermodynamics of a physical model implementing a Maxwell demon, Phys. Rev. Lett. 110, 040601 (2013).
- K. Ptaszyński and M. Esposito, Thermodynamics of quantum information flows, Phys. Rev. Lett. 122, 150603 (2019).
- 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).
- D. Palmqvist, L. Tesser, and J. Splettstoesser, Kinetic uncertainty relations for quantum transport, Phys. Rev. Lett. 135, 166302 (2025).
- T. Van Vu, Fundamental bounds on precision and response for quantum trajectory observables, PRX Quantum 6, 010343 (2025).
- D. Palmqvist, L. Tesser, and J. Splettstoesser, Combining kinetic and thermodynamic uncertainty relations in quantum transport, Quantum Sci. Technol. 10, 035059 (2025).
- K. Prech, G. T. Landi, F. Meier, N. Nurgalieva, P. P. Potts, R. Silva, and M. T. Mitchison, Optimal time estimation and the clock uncertainty relation for stochastic processes, Phys. Rev. X 15, 031068 (2025).
- N. Freitas and M. Esposito, Characterizing autonomous Maxwell demons, Phys. Rev. E 103, 032118 (2021).
- D. A. Bagrets and Yu. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade systems, Phys. Rev. B 67, 085316 (2003).
- C. Flindt, T. Novotný, A. Braggio, M. Sassetti, and A.-P. Jauho, Counting statistics of non-Markovian quantum stochastic processes, Phys. Rev. Lett. 100, 150601 (2008).
- Y. Utsumi, Full counting statistics of information content in the presence of Coulomb interaction, Phys. Rev. B 92, 165312 (2015).
- D. Andrieux, P. Gaspard, T. Monnai, and S. Tasaki, The fluctuation theorem for currents in open quantum systems, New J. Phys. 11, 043014 (2009).
- T. Fujisawa, T. Hayashi, R. Tomita, and Y. Hirayama, Bidirectional counting of single electrons, Science 312, 1634 (2006).
- B. Küng, C. Rössler, M. Beck, M. Marthaler, D. S. Golubev, Y. Utsumi, T. Ihn, and K. Ensslin, Irreversibility on the level of single-electron tunneling, Phys. Rev. X 2, 011001 (2012).
- A. Hofmann, V. F. Maisi, C. Rössler, J. Basset, T. Krähenmann, P. Märki, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider, Equilibrium free energy measurement of a confined electron driven out of equilibrium, Phys. Rev. B 93, 035425 (2016).
- A. Hofmann, V. F. Maisi, J. Basset, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and C. Jarzynski, Heat dissipation and fluctuations in a driven quantum dot, Physica Status Solidi (b) 254, 1600546 (2017).
- K. Chida, A. Fujiwara, and K. Nishiguchi, Seebeck effect in a nanometer-scale dot in a Si nanowire observed with electron counting statistics, Appl. Phys. Lett. 121, 183501 (2022).
- O.-P. Saira, Y. Yoon, T. Tanttu, M. Möttönen, D. V. Averin, and J. P. Pekola, Test of the Jarzynski and Crooks fluctuation relations in an electronic system, Phys. Rev. Lett. 109, 180601 (2012).
- J. V. Koski, T. Sagawa, O.-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T. Ala-Nissila, and J. P. Pekola, Distribution of entropy production in a single-electron box, Nat. Phys. 9, 644 (2013).
- O. Maillet, P. A. Erdman, V. Cavina, B. Bhandari, E. T. Mannila, J. T. Peltonen, A. Mari, F. Taddei, C. Jarzynski, V. Giovannetti, and J. P. Pekola, Optimal probabilistic work extraction beyond the free energy difference with a single-electron device, Phys. Rev. Lett. 122, 150604 (2019).
- R. Sánchez and M. Büttiker, Detection of single-electron heat transfer statistics, Europhys. Lett. 100, 47008 (2012).
- K. Chida, A. Andrieux, and K. Nishiguchi, Coulomb-mediated single-electron heat transfer statistics across capacitively coupled silicon nanodots, Commun. Phys. 9, 8 (2025).
- R. Sánchez, B. Sothmann, A. N. Jordan, and M. Büttiker, Correlations of heat and charge currents in quantum-dot thermoelectric engines, New J. Phys. 15, 125001 (2013).
- G. Schaller, Open Quantum Systems Far from Equilibrium (Springer, Cham, Switzerland, 2014).
- C. W. J. Beenakker and A. A. M. Staring, Theory of the thermopower of a quantum dot, Phys. Rev. B 46, 9667 (1992).
- D. Lenstra, Photon-number statistics in resonance fluorescence, Phys. Rev. A 26, 3369 (1982).
- R. Sánchez, G. Platero, and T. Brandes, Resonance fluorescence in transport through quantum dots: Noise properties, Phys. Rev. Lett. 98, 146805 (2007).
- K. Macieszczak, Ultimate kinetic uncertainty relation and optimal performance of stochastic clocks, arXiv:2407.09839.
- S. Saryal, S. Mohanta, and B. K. Agarwalla, Bounds on fluctuations for machines with broken time-reversal symmetry: A linear response study, Phys. Rev. E 105, 024129 (2022).
- R. D. Mayrhofer, C. Elouard, J. Splettstoesser, and A. N. Jordan, Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine, Phys. Rev. B 103, 075404 (2021).
- G. Fiusa, P. E. Harunari, A. S. Hegde, and G. T. Landi, Counting observables in stochastic excursions, arXiv:2505.06208.
- G. Fiusa, P. E. Harunari, A. S. Hegde, and G. T. Landi, A framework for fluctuating times and counting observables in stochastic excursions, arXiv:2506.05160.
- C. Van den Broeck and M. Esposito, Ensemble and trajectory thermodynamics: A brief introduction, Physica A 418, 6 (2015).
- B. Bhandari, G. Chiriacò, P. A. Erdman, R. Fazio, and F. Taddei, Thermal drag in electronic conductors, Phys. Rev. B 98, 035415 (2018).
- R. S. Whitney, Most efficient quantum thermoelectric at finite power output, Phys. Rev. Lett. 112, 130601 (2014).
- R. S. Whitney, Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output, Phys. Rev. B 91, 115425 (2015).
- J. B. Pendry, Quantum limits to the flow of information and entropy, J. Phys. A: Math. Gen. 16, 2161 (1983).
- Ya. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000).
- J. Monsel, M. Acciai, D. Palmqvist, N. Chiabrando, R. Sánchez, and J. Splettstoesser, Data and code for “Precision of an autonomous demon exploiting nonthermal resources and information”, Zenodo (2025), http://doi.org/10.5281/zenodo.17370450.
- J. Monsel, M. Acciai, R. Sánchez, and J. Splettstoesser, Data and code for “Autonomous demon exploiting heat and information at the trajectory level”, Zenodo (2024), http://doi.org/10.5281/zenodo.13740976.
- J. G. Skellam, The frequency distribution of the difference between two Poisson variates belonging to different populations, J. R. Stat. Soc. 109, 296 (1946).
- J. M. Horowitz and M. Esposito, Thermodynamics with continuous information flow, Phys. Rev. X 4, 031015 (2014).
- R. Takaki, M. L. Mugnai, and D. Thirumalai, Information flow, gating, and energetics in dimeric molecular motors, Proc. Natl. Acad. Sci. USA 119, e2208083119 (2022).