Two capacitor paradox
Its easier to think about this using the water pressure analogy. Imagine a large barrel full of water connected to another identical barrel. The first barrel is filled to the top whilst the second is empty. A valve is opened between the two barrels and they equalise with half of the water in each.<p>The initial energy is mgh and the final energy is 2 * (m/2 * g * h/2) = mgh/2 so half of then energy has disappeared. It is clear that work could have been done by the water moving between the two barrels (like in a hydro-electric power station).