Kinetic heterogeneity tightens thermodynamic bounds on spectra of Markov cycles
Abstract
Thermodynamic bounds on the spectrum of a Markov cycle are determined by quantities such as the cycle affinity and maximal escape rate, but do not distinguish cycles with different local rate profiles. In this work, we show that kinetic heterogeneity, through the geometric means of forward (G+) and backward (G-) rates, tightens the bound on oscillatory relaxation. Specifically, we prove that, for each winding sector of the eigenmodes, the oscillation frequency cannot exceed that of the uniform comparison cycle with rates G+ and G-. Combining with existing affinity-winding bounds, we also demonstrate a contracted region for the eigenvalues and shows that the boundary of Uhl-Seifert ellipse can be saturated if and only if cycles are uniform. Our proof provides a complex-analytic framework that unifies the kinetic and thermodynamic constraint.
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BibTeX
@misc{xu2026kinetic,
title = {{Kinetic heterogeneity tightens thermodynamic bounds on spectra of Markov cycles}},
author = {Rongxing Xu and Cuiling Meng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.22934},
eprint = {2608.22934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22934},
}
RIS
TY - UNPB
TI - Kinetic heterogeneity tightens thermodynamic bounds on spectra of Markov cycles
AU - Rongxing Xu
AU - Cuiling Meng
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2608.22934
UR - https://arxiv.org/abs/2608.22934
AB - Thermodynamic bounds on the spectrum of a Markov cycle are determined by quantities such as the cycle affinity and maximal escape rate, but do not distinguish cycles with different local rate profiles. In this work, we show that kinetic heterogeneity, through the geometric means of forward (G_+) and backward (G_-) rates, tightens the bound on oscillatory relaxation. Specifically, we prove that, for each winding sector of the eigenmodes, the oscillation frequency cannot exceed that of the uniform comparison cycle with rates G_+ and G_-. Combining with existing affinity-winding bounds, we also demonstrate a contracted region for the eigenvalues and shows that the boundary of Uhl-Seifert ellipse can be saturated if and only if cycles are uniform. Our proof provides a complex-analytic framework that unifies the kinetic and thermodynamic constraint.
ER -