Nonlocal Thermoelectric Transport in Degenerate Electron Systems
Abstract
When the characteristic length scales of transport become comparable to the carrier mean free path, the local constitutive description breaks down. We develop the Flux Derivative Formalism (FDF), a kinetic framework that provides a systematic route from the Boltzmann equation to nonlocal constitutive equations. We use it to derive coupled equations for charge and heat transport in isotropic electronic systems, together with boundary conditions derived consistently within this approach, yielding a closed macroscopic description that can be applied to complex geometries without solving the full Boltzmann problem. The explicit transport coefficients are derived for degenerate electronic systems within the Callaway model. A central result is that varying the relative strength of resistive and momentum-conserving collisions changes the transport coefficients but not the non-local constitutive structure, providing a continuous description from resistive-dominated transport to the collective hydrodynamic limit. The electronic heat equation takes a Guyer-Krumhansl form, whose predictions are validated against size-dependent thermal-transport measurements in Cu and Ni. For coupled thermoelectric transport, the resulting boundary-value problem determines the complete geometry-dependent transport matrix. Comparison with spatially resolved Boltzmann solutions confirms quantitative accuracy down to transverse dimensions comparable to the carrier mean free path. The theory predicts geometry-dependent Seebeck and Peltier coefficients while preserving Onsager reciprocity and the Kelvin relation.
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BibTeX
@misc{beardo2026nonlocal,
title = {{Nonlocal Thermoelectric Transport in Degenerate Electron Systems}},
author = {Albert Beardo and Adrián Ramos-Martín and Jordi Tur-Prats and F. Xavier Alvarez and Juan Camacho},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32272},
eprint = {2610.32272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32272},
}
RIS
TY - UNPB
TI - Nonlocal Thermoelectric Transport in Degenerate Electron Systems
AU - Albert Beardo
AU - Adrián Ramos-Martín
AU - Jordi Tur-Prats
AU - F. Xavier Alvarez
AU - Juan Camacho
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32272
UR - https://arxiv.org/abs/2610.32272
AB - When the characteristic length scales of transport become comparable to the carrier mean free path, the local constitutive description breaks down. We develop the Flux Derivative Formalism (FDF), a kinetic framework that provides a systematic route from the Boltzmann equation to nonlocal constitutive equations. We use it to derive coupled equations for charge and heat transport in isotropic electronic systems, together with boundary conditions derived consistently within this approach, yielding a closed macroscopic description that can be applied to complex geometries without solving the full Boltzmann problem. The explicit transport coefficients are derived for degenerate electronic systems within the Callaway model. A central result is that varying the relative strength of resistive and momentum-conserving collisions changes the transport coefficients but not the non-local constitutive structure, providing a continuous description from resistive-dominated transport to the collective hydrodynamic limit. The electronic heat equation takes a Guyer-Krumhansl form, whose predictions are validated against size-dependent thermal-transport measurements in Cu and Ni. For coupled thermoelectric transport, the resulting boundary-value problem determines the complete geometry-dependent transport matrix. Comparison with spatially resolved Boltzmann solutions confirms quantitative accuracy down to transverse dimensions comparable to the carrier mean free path. The theory predicts geometry-dependent Seebeck and Peltier coefficients while preserving Onsager reciprocity and the Kelvin relation.
ER -