Abstract: In this talk systems of reaction-diffusion equations are considered that can be written as gradient systems with respect to an entropy functional and a dissipation metric. The latter is given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. New methods for establishing the geodesic λ-convexity of the entropy functional by purely differential methods are discussed, thus circumventing arguments from mass transportation.