Abstract: 
We study a rescaling of the zerorange process with homogenous jump rates $g(k)=k^\alpha$ with arbitrary $\alpha\ge 1$. With a simultaneous rescaling of space, time and particle size, we identify the dynamical large deviations from the porous medium equation, using pathwise discretised regularity estimates to prove a version of the superexponential estimate in the spirit of the AubinLionsSimons lemma. Finally, we use the large deviation principle to give an expression of the porous medium equation as the gradient flow of the Boltzmann entropy with respect to a tailormade Wassersteintype distance. 
