Kharkiv Quantum Seminar

In any device, an effort to reduce the fluctuations of an output quantity is necessarily accompanied by an increase in entropy production, thereby lowering efficiency. This interplay is beautifully captured by the so-called Thermodynamic Uncertainty Relations (TURs), which set a lower bound on the relative uncertainty of a current for a given entropy-production rate [1-5].

TURs have been derived for various systems (e.g., classical [1-4], non-interacting quantum [5]). Studying violations of, for example, the classical TUR in a nanoscale device is particularly interesting [6], as it provides a proxy for the system's degree of quantum behaviour.

In this talk, we focus on the role of superconducting coherence in TUR violations [7].

To this aim, we consider hybrid systems consisting of one superconducting and two normal leads coupled to a central region containing localized levels. We first study the simplest setup yielding TUR violations, where the central region is a single-level quantum dot and only one normal lead is connected. In addition to the classical TUR [1-4], we consider the quantum TUR recently derived for coherent conductors [5]. We find that even this latter quantum TUR is violated (although to a smaller extent) as a result of the macroscopic phase coherence related to the superconducting condensate. To support this conclusion, we connect the second normal lead as a dephasing probe, demonstrating that the violation is directly correlated with the superconducting coherence, as measured by the dot's pair amplitude. When the central region is a Cooper-pair splitter, crossed Andreev processes introduce nonlocal superconducting correlations that further enhance the quantum-TUR violation. If time allows, we will also discuss the effects of Coulomb repulsion in the central region.

Finally, we present a quantum-hybrid TUR for systems with normal and superconducting leads in the large superconducting gap limit [7]. As expected, this TUR takes into account Andreev reflection processes and is never violated in the systems discussed in this talk.

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[2]  K. Macieszczak, K. Brandner, and J. P. Garrahan, Unified thermodynamic uncertainty relations in linear response, Phys. Rev Lett. 121, 130601 (2018)

[3] U. Seifert, From stochastic thermodynamics to thermodynamic inference, Annual Review of Condensed Matter Physics 10, 171 (2019).

[4] J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nature Physics 16, 15 (2020).

[5] K. Brandner and K. Saito, Thermodynamic uncertainty relations for coherent transport, Phys. Rev. Lett. 135, 046302 (2025).

[6] B. K. Agarwalla and D. Segal, Assessing the validity of the thermodynamic uncertainty relation in quantum systems, Phys. Rev. B 98, 155438 (2018).

[7] F. Mayo, N. Sobrino, R. Fazio, F. Taddei, and M. Governale, Thermodynamic Uncertainty Relation in Hybrid Normal-Superconducting Systems: The Role of superconducting coherence, arXiv:2506.02904 (2025).