WIAS Preprint No. 1650, (2011)

Geodesic convexity of the relative entropy in reversible Markov chains


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

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

Appeared in

  • Calc. Var. Partial Differ. Equ., 48 (2013) pp. 1-31.

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