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  • Open Access

Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence

Franco Mayo1,2,3, Nahual Sobrino3,*, Rosario Fazio3,4, Fabio Taddei5, and Michele Governale6

  • *Contact author: nsobrino@ictp.it
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Phys. Rev. Research 8, 013242 – Published 5 March, 2026

DOI: https://doi.org/10.1103/tfsv-fjzd

Abstract

Stability and efficiency are mutually exclusive in a thermodynamic process, e.g., in a thermal machine. Any effort to reduce the fluctuations of a certain output quantity is necessarily accompanied by an increase of entropy production, therefore lowering its 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 rate of entropy production. Their status in hybrid normal-superconducting (N-S) devices has remained unsettled. We show that, in the subgap regime, departures from the normal quantum TUR are governed by macroscopic superconducting coherence quantified by the pair amplitude, and that introducing a dephasing probe suppresses this coherence and restores the bound. We further derive a hybrid quantum TUR that is general for two-terminal N-S junctions in the Andreev regime: the inequality is never violated, is saturated only at vanishing current, and is related to the normal quantum bound under the replacement e→2e. For N-S quantum dot and Cooper-pair-splitter systems, we compute current and noise and show that deviations from the normal bound track the pair amplitude on the central region. The results establish a direct link between superconducting macroscopic coherence and nonequilibrium fluctuations and supply a general bound for the Andreev regime.

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Phys. Rev. Research 8, 013242– Published 5 March, 2026
  • Received 3 June 2025
  • Accepted 28 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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