- Open Access
Universal Relations between Thermoelectrics and Noise in Mesoscopic Transport across a Tunnel Junction
Phys. Rev. Lett. 136, 046301 – Published 26 January, 2026
DOI: https://doi.org/10.1103/h5ty-45rf
Abstract
We develop a unified theory of weakly probed differential observables for currents and noise in transport experiments. Our findings uncover a set of universal transport relations between thermoelectric and noise properties of a system probed through a tunnel contact, with the Wiedemann-Franz law being just one example of such universality between charge and heat currents. We apply this theory to various quantum systems, including multichannel Kondo, quantum Hall and Sachdev-Ye-Kitaev quantum dots, resonant impurity, and two-stage Kondo models and demonstrate that each of the microscopic theories is characterized by a set of universal relations connecting conductance and thermoelectrics with noise. Violations of these relations indicate additional energy scales emerging in a system.
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References (128)
- R. Scheibner, H. Buhmann, D. Reuter, M. N. Kiselev, and L. W. Molenkamp, Thermopower of a Kondo spin-correlated quantum dot, Phys. Rev. Lett. 95, 176602 (2005).
- Y. Yamauchi, K. Sekiguchi, K. Chida, T. Arakawa, S. Nakamura, K. Kobayashi, T. Ono, T. Fujii, and R. Sakano, Evolution of the Kondo effect in a quantum dot probed by shot noise, Phys. Rev. Lett. 106, 176601 (2011).
- I. V. Borzenets, J. Shim, J. C. H. Chen, A. Ludwig, A. D. Wieck, S. Tarucha, H.-S. Sim, and M. Yamamoto, Observation of the Kondo screening cloud, Nature (London) 579, 210 (2020).
- S. F. Godijn, S. Möller, H. Buhmann, L. W. Molenkamp, and S. A. van Langen, Thermopower of a chaotic quantum dot, Phys. Rev. Lett. 82, 2927 (1999).
- P. Barthold, F. Hohls, N. Maire, K. Pierz, and R. J. Haug, Enhanced shot noise in tunneling through a stack of coupled quantum dots, Phys. Rev. Lett. 96, 246804 (2006).
- N. Hartman, C. Olsen, S. Lüscher, M. Samani, S. Fallahi, G. C. Gardner, M. Manfra, and J. Folk, Direct entropy measurement in a mesoscopic quantum system, Nat. Phys. 14, 1083 (2018).
- J. K. Dong, Y. Tokiwa, S. L. Bud’ko, P. C. Canfield, and P. Gegenwart, Anomalous reduction of the Lorenz ratio at the quantum critical point in YbAgGe, Phys. Rev. Lett. 110, 176402 (2013).
- L. Chen, D. T. Lowder, E. Bakali, A. M. Andrews, W. Schrenk, M. Waas, R. Svagera, G. Eguchi, L. Prochaska, Y. Wang, C. Setty, S. Sur, Q. Si, S. Paschen, and D. Natelson, Shot noise in a strange metal, Science 382, 907 (2023).
- Y. Wang, C. Setty, S. Sur, L. Chen, S. Paschen, D. Natelson, and Q. Si, Shot noise and universal Fano factor as a characterization of strongly correlated metals, Phys. Rev. Res. 6, L042045 (2024).
- A. Gleis, S. S. B. Lee, G. Kotliar, and J. von Delft, Dynamical scaling and Planckian dissipation due to heavy-fermion quantum criticality, Phys. Rev. Lett. 134, 106501 (2025).
- J. Mravlje and A. Georges, Thermopower and entropy: Lessons from , Phys. Rev. Lett. 117, 036401 (2016).
- S. Sachdev, Bekenstein-Hawking entropy and strange metals, Phys. Rev. X 5, 041025 (2015).
- R. A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen, and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95, 155131 (2017).
- G. A. Inkof, J. M. C. Küppers, J. M. Link, B. Goutéraux, and J. Schmalian, Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points, J. High Energy Phys. 11 (2020) 088.
- T. Martin, Noise in mesoscopic physics, in Nanophysics: Coherence and Transport, Les Houches, Session LXXXI, edited by H. Bouchiat, Y. Gefen, S. Guéron, G. Montambaux, and J. Dalibard (Elsevier, New York, 2005), p. 283, 10.1016/S0924-8099(05)80047-2.
- O. S. Lumbroso, L. Simine, A. Nitzan, D. Segal, and O. Tal, Electronic noise due to temperature differences in atomic-scale junctions, Nature (London) 562, 240 (2018).
- E. Sivre, H. Duprez, A. Anthore, A. Aassime, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, Electronic heat flow and thermal shot noise in quantum circuits, Nat. Commun. 10, 5638 (2019).
- S. Larocque, E. Pinsolle, C. Lupien, and B. Reulet, Shot noise of a temperature-biased tunnel junction, Phys. Rev. Lett. 125, 106801 (2020).
- M. G. Vavilov and A. D. Stone, Failure of the Wiedemann-Franz law in mesoscopic conductors, Phys. Rev. B 72, 205107 (2005).
- M. A. Tanatar, J. Paglione, C. Petrovic, and L. Taillefer, Anisotropic violation of the Wiedemann-Franz law at a quantum critical point, Science 316, 1320 (2007).
- B. Kubala, J. König, and J. Pekola, Violation of the Wiedemann-Franz law in a single-electron transistor, Phys. Rev. Lett. 100, 066801 (2008).
- M. Tikhanovskaya, H. Guo, S. Sachdev, and G. Tarnopolsky, Excitation spectra of quantum matter without quasiparticles. I. Sachdev-Ye-Kitaev models, Phys. Rev. B 103, 075141 (2021).
- D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids, Rev. Mod. Phys. 94, 035004 (2022).
- N. C. van der Vaart, S. F. Godijn, Y. V. Nazarov, C. J. P. M. Harmans, J. E. Mooij, L. W. Molenkamp, and C. T. Foxon, Resonant tunneling through two discrete energy states, Phys. Rev. Lett. 74, 4702 (1995).
- D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Kondo effect in a single-electron transistor, Nature (London) 391, 156 (1998).
- D. Goldhaber-Gordon, J. Göres, M. A. Kastner, H. Shtrikman, D. Mahalu, and U. Meirav, From the Kondo regime to the mixed-valence regime in a single-electron transistor, Phys. Rev. Lett. 81, 5225 (1998).
- A. Nauen, I. Hapke-Wurst, F. Hohls, U. Zeitler, R. J. Haug, and K. Pierz, Shot noise in self-assembled InAs quantum dots, Phys. Rev. B 66, 161303(R) (2002).
- A. Nauen, F. Hohls, N. Maire, K. Pierz, and R. J. Haug, Shot noise in tunneling through a single quantum dot, Phys. Rev. B 70, 033305 (2004).
- E. Slot, M. A. Holst, H. S. J. van der Zant, and S. V. Zaitsev-Zotov, One-dimensional conduction in charge-density-wave nanowires, Phys. Rev. Lett. 93, 176602 (2004).
- H. B. Heersche, Z. de Groot, J. A. Folk, H. S. J. van der Zant, C. Romeike, M. R. Wegewijs, L. Zobbi, D. Barreca, E. Tondello, and A. Cornia, Electron transport through single molecular magnets, Phys. Rev. Lett. 96, 206801 (2006).
- B. Huard, J. A. Sulpizio, N. Stander, K. Todd, B. Yang, and D. Goldhaber-Gordon, Transport measurements across a tunable potential barrier in graphene, Phys. Rev. Lett. 98, 236803 (2007).
- E. A. Osorio, T. Bjørnholm, J.-M. Lehn, M. Ruben, and H. S. J. van der Zant, Single-molecule transport in three-terminal devices, J. Phys. Condens. Matter 20, 374121 (2008).
- H. Prüser, M. Wenderoth, P. E. Dargel, A. Weismann, R. Peters, T. Pruschke, and R. G. Ulbrich, Long-range Kondo signature of a single magnetic impurity, Nat. Phys. 7, 203 (2011).
- M. L. Perrin, C. J. O. Verzijl, C. A. Martin, A. J. Shaikh, R. Eelkema, J. H. van Esch, J. M. van Ruitenbeek, J. M. Thijssen, H. S. J. van der Zant, and D. Dulić, Large tunable image-charge effects in single-molecule junctions, Nat. Nanotechnol. 8, 282 (2013).
- E. Burzurí, Y. Yamamoto, M. Warnock, X. Zhong, K. Park, A. Cornia, and H. S. J. van der Zant, Franck-Condon blockade in a single-molecule transistor, Nano Lett. 14, 3191 (2014).
- Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. D. Parmentier, A. Cavanna, and F. Pierre, Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states, Nature (London) 526, 233 (2015).
- Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, and F. Pierre, Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit, Science 360, 1315 (2018).
- P. Gehring, J. M. Thijssen, and H. S. J. van der Zant, Single-molecule quantum-transport phenomena in break junctions, Nat. Rev. Phys. 1, 381 (2019).
- X. Guo, Q. Zhu, L. Zhou, W. Yu, W. Lu, and W. Liang, Evolution and universality of two-stage Kondo effect in single manganese phthalocyanine molecule transistors, Nat. Commun. 12, 1566 (2021).
- O. Dani, R. Hussein, J. C. Bayer, S. Kohler, and R. J. Haug, Temperature-dependent broadening of coherent current peaks in InAs double quantum dots, Commun. Phys. 5, 5638 (2022).
- W. Pouse, L. Peeters, C. L. Hsueh, U. Gennser, A. Cavanna, M. A. Kastner, A. K. Mitchell, and D. Goldhaber-Gordon, Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit, Nat. Phys. 19, 492 (2023).
- C. Piquard, P. Glidic, C. Han, A. Aassime, A. Cavanna, U. Gennser, Y. Meir, E. Sela, A. Anthore, and F. Pierre, Observing the universal screening of a Kondo impurity, Nat. Commun. 14, 7263 (2023).
- L. E. Anderson, A. Laitinen, A. Zimmerman, T. Werkmeister, L. Shackleton, A. Kruchkov, T. Taniguchi, K. Watanabe, S. Sachdev, and P. Kim, Magneto-thermoelectric transport in graphene quantum dot with strong correlations, Phys. Rev. Lett. 132, 246502 (2024).
- See Supplemental Material http://link.aps.org/supplemental/10.1103/h5ty-45rf for discussion on connections to experimental setups, applications of the developed theory to various models, and generalization beyond the linear response regime, which includes Refs. [45–60].
- L. Spietz, K. W. Lehnert, I. Siddiqi, and R. J. Schoelkopf, Primary electronic thermometry using the shot noise of a tunnel junction, Science 300, 1929 (2003).
- P. Février and J. Gabelli, Tunneling time probed by quantum shot noise, Nat. Commun. 9, 4940 (2018).
- I. Tamir, V. Caspari, D. Rolf, C. Lotze, and K. J. Franke, Shot-noise measurements of single-atom junctions using a scanning tunneling microscope, Rev. Sci. Instrum. 93, 023702 (2022).
- K. Flensberg, Capacitance and conductance of mesoscopic systems connected by quantum point contacts, Phys. Rev. B 48, 11156 (1993).
- K. A. Matveev, Coulomb blockade at almost perfect transmission, Phys. Rev. B 51, 1743 (1995).
- G. Farahi, C.-L. Chiu, X. Liu, Z. Papic, K. Watanabe, T. Taniguchi, M. P. Zaletel, and A. Yazdani, Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels, Nat. Phys. 19, 1482 (2023).
- Y. Hu, Y.-C. Tsui, M. He, U. Kamber, T. Wang, A. S. Mohammadi, K. Watanabe, T. Taniguchi, Z. Papić, M. P. Zaletel, and A. Yazdani, High-resolution tunnelling spectroscopy of fractional quantum Hall states, Nat. Phys. 21, 716 (2025).
- N. V. Gnezdilov, J. A. Hutasoit, and C. W. J. Beenakker, Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model, Phys. Rev. B 98, 081413(R) (2018).
- A. Manaparambil, A. Weichselbaum, J. von Delft, and I. Weymann, Nonequilibrium steady-state thermoelectrics of Kondo-correlated quantum dots, Phys. Rev. B 111, 035445 (2025).
- D. N. Aristov, Luttinger liquids with curvature: Density correlations and Coulomb drag effect, Phys. Rev. B 76, 085327 (2007).
- T. K. T. Nguyen, M. N. Kiselev, and V. E. Kravtsov, Thermoelectric transport through a quantum dot: Effects of asymmetry in Kondo channels, Phys. Rev. B 82, 113306 (2010).
- M. Pustilnik and L. I. Glazman, Kondo effect in real quantum dots, Phys. Rev. Lett. 87, 216601 (2001).
- K. P. Wójcik and I. Weymann, Thermopower of strongly correlated T-shaped double quantum dots, Phys. Rev. B 93, 085428 (2016).
- K. Brown, M. Crisan, and I. Ţifrea, Transport and current noise characteristics of a T-shape double-quantum-dot system, J. Phys. Condens. Matter 21, 215604 (2009).
- D. B. Karki, Wiedemann-Franz law in scattering theory revisited, Phys. Rev. B 102, 115423 (2020).
- A. Oguri and A. C. Hewson, Higher-order Fermi-liquid corrections for an Anderson impurity away from half filling, Phys. Rev. Lett. 120, 126802 (2018).
- 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).
- F. Battista, F. Haupt, and J. Splettstoesser, Correlations between charge and energy current in ac-driven coherent conductors, J. Phys. Conf. Ser. 568, 052008 (2014).
- A. Crépieux and F. Michelini, Mixed, charge and heat noises in thermoelectric nanosystems, J. Phys. Condens. Matter 27, 015302 (2014).
- P. Jacquod, R. S. Whitney, J. Meair, and M. Büttiker, Onsager relations in coupled electric, thermoelectric, and spin transport: The tenfold way, Phys. Rev. B 86, 155118 (2012).
- F. Mazza, R. Bosisio, G. Benenti, V. Giovannetti, R. Fazio, and F. Taddei, Thermoelectric efficiency of three-terminal quantum thermal machines, New J. Phys. 16, 085001 (2014).
- 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. V. Andreev and K. A. Matveev, Coulomb blockade oscillations in the thermopower of open quantum dots, Phys. Rev. Lett. 86, 280 (2001).
- T. K. T. Nguyen and M. N. Kiselev, Thermoelectric transport in a three-channel charge Kondo circuit, Phys. Rev. Lett. 125, 026801 (2020).
- T. K. T. Nguyen, H. Q. Nguyen, and M. N. Kiselev, Thermoelectric transport across a tunnel contact between two charge Kondo circuits: Beyond perturbation theory, Phys. Rev. B 109, 115139 (2024).
- A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University Press, New York, 2011), 10.1017/CBO9781139003667.
- A. Popoff, J. Rech, T. Jonckheere, L. Raymond, B. Grémaud, S. Malherbe, and T. Martin, Scattering theory of non-equilibrium noise and delta T current fluctuations through a quantum dot, J. Phys. Condens. Matter 34, 185301 (2022).
- J. P. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021).
- L. Onsager, Reciprocal relations in irreversible processes. I, Phys. Rev. 37, 405 (1931).
We assume that the voltage bias is applied to the lead, while the system is grounded. We also consider the lead’s chemical potential shift by a positive voltage bias. This choice is arbitrary; for a negative bias, one can replace in the corresponding derivatives.
- P. Eymeoud and A. Crepieux, Mixed electrical-heat noise spectrum in a quantum dot, Phys. Rev. B 94, 205416 (2016).
- A. I. Pavlov and M. N. Kiselev, Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport, arXiv:2508.13098.
- L. Onsager, Reciprocal relations in irreversible processes. II, Phys. Rev. 38, 2265 (1931).
- K. A. Matveev and A. V. Andreev, Thermopower of a single-electron transistor in the regime of strong inelastic cotunneling, Phys. Rev. B 66, 045301 (2002).
Because of nonlinear effects, the thermopower at the finite voltage and finite temperature bias is not necessarily zero at the particle-hole symmetric point [1, 80], which is beyond the linear response theory.
- D. B. Karki and M. N. Kiselev, Thermoelectric transport through a Kondo impurity, Phys. Rev. B 96, 121403(R) (2017).
- G. A. R. van Dalum, A. K. Mitchell, and L. Fritz, Wiedemann-Franz law in a non-Fermi liquid and Majorana central charge: Thermoelectric transport in a two-channel Kondo system, Phys. Rev. B 102, 041111(R) (2020).
- I. L. Aleiner and L. I. Glazman, Mesoscopic charge quantization, Phys. Rev. B 57, 9608 (1998).
- M. N. Kiselev, Generalized Wiedemann-Franz law in a two-site charge Kondo circuit: Lorenz ratio as a manifestation of the orthogonality catastrophe, Phys. Rev. B 108, L081108 (2023).
- F. Stäbler and E. Sukhorukov, Mesoscopic heat multiplier and fractionalizer, Phys. Rev. B 108, 235405 (2023).
- A. I. Pavlov and M. N. Kiselev, Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade, Phys. Rev. B 103, L201107 (2021).
The Lorenz ratio gives direct access to the scaling dimension of the leading irrelevant operator through the parameter , a related property of the delta- noise for quantum Hall devices is discussed in [87, 88, 89, 90].
- G. Zhang, I. V. Gornyi, and C. Spånslätt, Delta- noise for weak tunneling in one-dimensional systems: Interactions versus quantum statistics, Phys. Rev. B 105, 195423 (2022).
- N. Schiller, Y. Oreg, and K. Snizhko, Extracting the scaling dimension of quantum Hall quasiparticles from current correlations, Phys. Rev. B 105, 165150 (2022).
- H. Ebisu, N. Schiller, and Y. Oreg, Fluctuations in heat current and scaling dimension, Phys. Rev. Lett. 128, 215901 (2022).
- M. Acciai, G. Zhang, and C. Spånslätt, Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias, SciPost Phys. 18, 058 (2025).
- P. W. Anderson, Infrared catastrophe in Fermi gases with local scattering potentials, Phys. Rev. Lett. 18, 1049 (1967).
- G. D. Mahan, Excitons in metals: Infinite hole mass, Phys. Rev. 163, 612 (1967).
- A. Furusaki and K. A. Matveev, Theory of strong inelastic cotunneling, Phys. Rev. B 52, 16676 (1995).
- A. Kitaev and S. J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, J. High Energy Phys. 05 (2018) 183.
- M. Berkooz and O. Mamroud, A cordial introduction to double scaled SYK, Rep. Prog. Phys. 88, 036001 (2025).
- A. Altland, K. W. Kim, T. Micklitz, M. Rezaei, J. Sonner, and J. J. M. Verbaarschot, Quantum chaos on edge, Phys. Rev. Res. 6, 033286 (2024).
- M. N. Kiselev, Universal scaling functions for a quantum transport through single-site and double-site charge Kondo circuits, in Lecture Notes in Physics (to be published).
The divergence of the DOS in the DSSYK model exists for the conformal saddle-point solution and disappears in the infrared regularization of the saddle point. The theory is well behaved for large and large as long as . The effective infrared theory in this regime coincides with the conventional SYK Schwarzian theory up to parametric prefactors and has the same energy scaling [95].
- V. Gurarie, Logarithmic operators and logarithmic conformal field theories, J. Phys. A 46, 494003 (2013).
- L. Van Hove, The occurrence of singularities in the elastic frequency distribution of a crystal, Phys. Rev. 89, 1189 (1953).
- D. V. Efremov, A. Shtyk, A. W. Rost, C. Chamon, A. P. Mackenzie, and J. J. Betouras, Multicritical Fermi surface topological transitions, Phys. Rev. Lett. 123, 207202 (2019).
- A. Chandrasekaran, A. Shtyk, J. J. Betouras, and C. Chamon, Catastrophe theory classification of Fermi surface topological transitions in two dimensions, Phys. Rev. Res. 2, 013355 (2020).
- Noah F. Q. Yuan and L. Fu, Classification of critical points in energy bands based on topology, scaling, and symmetry, Phys. Rev. B 101, 125120 (2020).
- A. Zervou, D. V. Efremov, and J. J. Betouras, Fate of density waves in the presence of a higher-order van Hove singularity, Phys. Rev. Res. 5, L042006 (2023).
- A. Shtyk, G. Goldstein, and C. Chamon, Electrons at the monkey saddle: A multicritical Lifshitz point, Phys. Rev. B 95, 035137 (2017).
- A. Piriou, N. Jenkins, C. Berthod, I. Maggio-Aprile, and Ø. Fischer, First direct observation of the Van Hove singularity in the tunnelling spectra of cuprates, Nat. Commun. 2, 221 (2011).
- K.-S. Chen, S. Pathak, S.-X. Yang, S.-Q. Su, D. Galanakis, K. Mikelsons, M. Jarrell, and J. Moreno, Role of the van Hove singularity in the quantum criticality of the Hubbard model, Phys. Rev. B 84, 245107 (2011).
- M. E. Barber, A. S. Gibbs, Y. Maeno, A. P. Mackenzie, and C. W. Hicks, Resistivity in the vicinity of a van Hove singularity: under uniaxial pressure, Phys. Rev. Lett. 120, 076602 (2018).
- V. C. Stangier, E. Berg, and J. Schmalian, Breakdown of the Wiedemann-Franz law at the Lifshitz point of strained , Phys. Rev. B 105, 115113 (2022).
- T. K. T. Nguyen, J. Rech, T. Martin, and M. N. Kiselev, Noises in a two-channel charge Kondo model, arXiv:2511.02590.
- C. Mora, P. Vitushinsky, X. Leyronas, A. A. Clerk, and K. Le Hur, Theory of nonequilibrium transport in the Kondo regime, Phys. Rev. B 80, 155322 (2009).
- C. Mora, C. P. Moca, J. von Delft, and G. Zaránd, Fermi-liquid theory for the single-impurity Anderson model, Phys. Rev. B 92, 075120 (2015).
- 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).
- 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).
- Y. Kleeorin, H. Thierschmann, H. Buhmann, A. Georges, L. W. Molenkamp, and Y. Meir, How to measure the entropy of a mesoscopic system via thermoelectric transport, Nat. Commun. 10, 5801 (2019).
- C. Han, Z. Iftikhar, Y. Kleeorin, A. Anthore, F. Pierre, Y. Meir, A. K. Mitchell, and E. Sela, Fractional entropy of multichannel Kondo systems from conductance-charge relations, Phys. Rev. Lett. 128, 146803 (2022).
- A. Kruchkov, A. A. Patel, P. Kim, and S. Sachdev, Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments, Phys. Rev. B 101, 205148 (2020).
- J. P. Pekola, Towards quantum thermodynamics in electronic circuits, Nat. Phys. 11, 118 (2015).
- G. Jaliel, R. K. Puddy, R. Sánchez, A. N. Jordan, B. Sothmann, I. Farrer, J. P. Griffiths, D. A. Ritchie, and C. G. Smith, Experimental realization of a quantum dot energy harvester, Phys. Rev. Lett. 123, 117701 (2019).
- R. Sánchez, B. Sothmann, and A. N. Jordan, Chiral thermoelectrics with quantum Hall edge states, Phys. Rev. Lett. 114, 146801 (2015).
- J. Rech, T. Jonckheere, B. Grémaud, and T. Martin, Negative delta-T noise in the fractional quantum Hall effect, Phys. Rev. Lett. 125, 086801 (2020).
- G. Rebora, J. Rech, D. Ferraro, T. Jonckheere, T. Martin, and M. Sassetti, Delta- noise for fractional quantum Hall states at different filling factor, Phys. Rev. Res. 4, 043191 (2022).
- K. Iyer, J. Rech, T. Jonckheere, L. Raymond, B. Grémaud, and T. Martin, Colored delta- noise in fractional quantum Hall liquids, Phys. Rev. B 108, 245427 (2023).
- G. Zhang, I. Gornyi, and Y. Gefen, Landscapes of an out-of-equilibrium anyonic sea, Phys. Rev. Lett. 134, 096303 (2025).
- G. Zhang, I. Gornyi, and Y. Gefen, Effective linear response in non-equilibrium anyonic systems, arXiv:2510.03985.
- J.-P. Brantut, C. Grenier, J. Meineke, D. Stadler, S. Krinner, C. Kollath, T. Esslinger, and A. Georges, A thermoelectric heat engine with ultracold atoms, Science 342, 713 (2013).
- S. Häusler, P. Fabritius, J. Mohan, M. Lebrat, L. Corman, and T. Esslinger, Interaction-assisted reversal of thermopower with ultracold atoms, Phys. Rev. X 11, 021034 (2021).
- F. Bauer, J. Heyder, E. Schubert, D. Borowsky, D. Taubert, B. Bruognolo, D. Schuh, W. Wegscheider, J. von Delft, and S. Ludwig, Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts, Nature (London) 501, 73 (2013).