  We investigate maximal potential energy dissipation as a selection criterion
for subsolutions (coarse grained solutions) in the setting of the unstable
Muskat problem. We show that both, imposing this criterion on the level of
convex integration subsolutions, and the strategy of Otto based on a relaxation
via minimizing movements, lead to the same nonlocal conservation law. Our main
result shows that this equation admits an entropy solution for unstable initial
data with an analytic interface.
