Geodesic convexity of the relative entropy in reversible Markov chains
- Mielke, Alexander
2010 Mathematics Subject Classification
- 60J27 53C21 53C23 82B35
- Markov chain, detailed balance, relative entropy, Onsager matrix, harmonic mean, geodesic convexity
We consider finite-dimensional, time-continuous Markov chains satisfying the detailed balance condition as gradient systems with the relative entropy E as driving functional. The Riemannian metric is defined via its inverse matrix called the Onsager matrix K. We provide methods for establishing geodesic λ-convexity of the entropy and treat several examples including some more general nonlinear reaction systems
- Calc. Var. Partial Differ. Equ., 48 (2013) pp. 1-31.