Thermodynamic Uncertainty Relation in Hybrid Normal-Superconducting Systems: The Role of Superconducting Coherence
In any device, reducing output fluctuations costs entropy production, lowering efficiency. Thermodynamic Uncertainty Relations (TURs) quantify this trade‑off by bounding current fluctuations for a given entropy production rate. They are well understood in classical and some quantum systems, and violations of the classical TUR in nanoscale conductors are used as a proxy for “how quantum” a device is.
This work studies how superconducting coherence affects such violations. The setup is a hybrid system: one superconducting and two normal leads coupled to a central region with localized levels. First, a minimal geometry is considered: a single‑level quantum dot with one normal and one superconducting lead. Besides the classical TUR, a quantum TUR for coherent conductors is tested. Remarkably, even this quantum TUR is violated, though less strongly, due to macroscopic phase coherence of the superconducting condensate.
To confirm the role of coherence, a second normal lead is used as a dephasing probe. Increasing its coupling suppresses superconducting coherence (tracked via the dot’s pair amplitude) and correspondingly weakens the quantum‑TUR violation. Extending the central region to a Cooper‑pair splitter, crossed Andreev reflection yields nonlocal superconducting correlations that further enhance the violation.
Finally, a new hybrid quantum TUR is derived for normal–superconducting systems in the large‑gap limit.
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