For reversible mean-field dynamics on finite state spaces, a positive entropic Ricci curvature bound implies modified logarithmic Sobolev, Talagrand transport-entropy and exponential entropy decay inequalities.
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Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
For reversible mean-field dynamics on finite state spaces, a positive entropic Ricci curvature bound implies modified logarithmic Sobolev, Talagrand transport-entropy and exponential entropy decay inequalities.