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.

arXiv comment15 pages, 3 figures