Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards

I. R. A. C. Lucena; T. J. A. Mori; M. M. Soares; D. Bazeia; A. R. Rocha

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arXiv · 2609.27065

Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards

I. R. A. C. Lucena·T. J. A. Mori·M. M. Soares·D. Bazeia·A. R. Rocha

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Abstract

We investigate how particle-hole symmetry, quantum interference, and tunnel barriers shape thermodynamic uncertainty relations in chaotic Andreev billiards. Using random-matrix theory and the Mahaux-Weidenmüller scattering approach, we study charge conductance and shot noise across the four Altland-Zirnbauer symmetry classes, from the single-channel extreme quantum limit to the multichannel semiclassical regime and from ideal to opaque contacts. We characterize thermodynamic precision through two complementary ensemble observables: either by averaging the sample-resolved noise-to-conductance ratio, or from the separately averaging noise and conductance. Their pronounced discrepancy in the extreme quantum regime reveals the non-self-averaging character of mesoscopic transport and persists over a broad range of barrier transparencies. For ideal contacts, the first provides a sensitive fingerprint of the Altland-Zirnbauer symmetry class. In the opaque regime, this hierarchy changes. Despite these strong symmetry- and barrier-dependent effects, the standard thermodynamic uncertainty relation remains satisfied throughout all regimes investigated. Our results establish thermodynamic uncertainty as a symmetry-sensitive probe of universal transport in chaotic normal-superconducting systems.

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I. R. A. C. Lucena, T. J. A. Mori, M. M. Soares, D. Bazeia, A. R. Rocha. 2026-09-22. Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards. https://arxiv.org/abs/2609.27065

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