Work

Thermodynamic Geometric Constraint on the Spectrum of Markov Rate Matrices

Year: 2025

Type: article

Abstract: The spectrum of Markov generators encodes physical information beyond simple decay and oscillation, which reflects irreversibility and governs the structure of correlation functions. In this Letter, we prove an ellipse theorem that provides a universal thermodynamic geometric constraint on the spectrum of Markov rate matrices. The theorem states that all eigenvalues lie within a specific ellipse in the complex plane. In particular, the imaginary parts of the spectrum, which indicate oscillatory modes, are bounded by the maximum thermodynamic force associated with individual transitions. This spectral bound further constrains the initial short-time behavior of correlation functions between two arbitrary observables. Finally, we compare our result with a previously proposed conjecture, which remains an open problem and warrants further investigation.

Source: Physical Review Letters

DOI: 10.1103/z4t2-18cx

Authors: Guo-Hua Xu, Artemy Kolchinsky, Jean-Charles Delvenne, Sosuke Ito

Institutions: The University of Tokyo, Universitat Pompeu Fabra, Kyoto University, UCLouvain

Language: English

Topic: Advanced Thermodynamics and Statistical Mechanics

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,750