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Second largest eigenvalue does not bound stationary entropy production

  • Naoto Shiraishi
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Abstract

We examine the spectral dissipation-coherence trade-off inequality conjectured by Oberreiter {\it et al}. [Phys. Rev. E 106, 014106 (2022)], stating that the coherent number, defined from the second largest eigenvalue, provides a lower bound on the stationary entropy production per unit oscillation. We disprove this conjecture by explicitly constructing a counterexample, which accompanies finite coherent number with vanishing stationary entropy production. This model also excludes a wide class of thermodynamic bound with the real and imaginary parts of the second largest eigenvalue of the transition rate matrix. Our result implies that the second largest eigenvalue does not necessarily characterize the degree of coherent oscillation.

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Cite

BibTeXRIS
BibTeX
@misc{shiraishi2026second,
  title = {{Second largest eigenvalue does not bound stationary entropy production}},
  author = {Naoto Shiraishi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34352},
  eprint = {2609.34352},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34352},
}
RIS
TY  - UNPB
TI  - Second largest eigenvalue does not bound stationary entropy production
AU  - Naoto Shiraishi
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34352
UR  - https://arxiv.org/abs/2609.34352
AB  - We examine the spectral dissipation-coherence trade-off inequality conjectured by Oberreiter {\it et al}. [Phys. Rev. E 106, 014106 (2022)], stating that the coherent number, defined from the second largest eigenvalue, provides a lower bound on the stationary entropy production per unit oscillation. We disprove this conjecture by explicitly constructing a counterexample, which accompanies finite coherent number with vanishing stationary entropy production. This model also excludes a wide class of thermodynamic bound with the real and imaginary parts of the second largest eigenvalue of the transition rate matrix. Our result implies that the second largest eigenvalue does not necessarily characterize the degree of coherent oscillation.
ER  -