A gradient flow approach to the Boltzmann equation

We show that the spatially homogeneous Boltzmann equation (with constant collision kernel) evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures. This geometry is given by a new notion of distance between probability measures, which takes the collision process into account. As a first application, we obtain a novel time-discrete approximation scheme for the homogeneous Boltzmann equation.

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