Thermodynamic uncertainty relations in quantum normal-superconductor hybrid systems

The effort to reduce fluctuations of an output quantity in a device necessarily results in an increase in entropy production, thus lowering efficiency. This interplay is formally captured by so-called Thermodynamic Uncertainty Relations (TURs), which set a lower bound on the relative uncertainty of, eg, a transport current for a given entropy-production rate. TURs have been derived for various systems (e.g., classical and non-interacting quantum). Studying violations of, for example, the classical TUR for transport in a nanoscale device is particularly interesting, as it provides a proxy measure for the system's degree of quantumness. See [1] for more information.

In this project, we will test for the possibility of TUR violations in normal-superconductor hybrid systems using nonequilibrium-quantum-transport calculations. The setup will consist of superconducting and normal leads connected to a central nanoscale region [2]. The results will shed light on the role of superconductivity in the trade-off between the precision of an output current and the entropy production rate.

[1] JM Horowitz, TR Gingrich, Nat. Phys. 16, 15 (2020). DOI: 10.1038/s41567-019-0702-6

[2] F Mayo et al., arXiv:2506.02904.

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