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PreprintCC BY 4.0arXiv

Transport Determines Spectral Distance in Mesoscopic Thermodynamics

  • Giorgio SONNINO
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Abstract

We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric G=2g, where g denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is √(1+ZT)+√(ZT). Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.

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Cite

BibTeXRIS
BibTeX
@misc{sonnino2026transport,
  title = {{Transport Determines Spectral Distance in Mesoscopic Thermodynamics}},
  author = {Giorgio SONNINO},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16752},
  eprint = {2610.16752},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16752},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Transport Determines Spectral Distance in Mesoscopic Thermodynamics
AU  - Giorgio SONNINO
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.16752
UR  - https://arxiv.org/abs/2610.16752
AB  - We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric G=2g, where g denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is √(1+ZT)+√(ZT). Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.
ER  -