Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards
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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BibTeX
@misc{lucena2026thermodynamic,
title = {{Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards}},
author = {I. R. A. C. Lucena and T. J. A. Mori and M. M. Soares and D. Bazeia and A. R. Rocha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27065},
eprint = {2609.27065},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27065},
}
RIS
TY - UNPB
TI - Thermodynamic Uncertainty Relations in Chaotic Andreev Billiards
AU - I. R. A. C. Lucena
AU - T. J. A. Mori
AU - M. M. Soares
AU - D. Bazeia
AU - A. R. Rocha
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27065
UR - https://arxiv.org/abs/2609.27065
AB - 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.
ER -