  Using the solution phase space method, we investigate the thermodynamics of
black holes in Einstein-aether-Maxwell theory, for which the traditional Wald
method (covariant phase space method) fails. We show the first laws of
thermodynamics and definitive entropy expressions at both Killing and universal
horizons for some examples of exact black hole solutions, including
3-dimensional static charged quasi-BTZ black hole, two 4-dimensional static
charged black holes and 3-dimensional rotating solution. At Killing horizons
the entropies are exactly one quarter of the horizon area, but at universal
horizons of 3-dimensional black holes, the entropies have a corrected term in
addition to the one proportional to the horizon area.
