  A subsystem of an entangled ground state is in a mixed state. Thus, if we
isolate this subsystem from its surroundings we may be able to extract work
applying unitary transformations, up to a maximal amount which is called
ergotropy. Once this work has been extracted, the subsystem will still contain
some bound energy above its local ground state, which can provide valuable
information about the entanglement structure. We show that the bound energy for
half a free fermionic chain decays as the square of the entanglement entropy
divided by the chain length, thus approaching zero for large system sizes, and
we conjecture that this relation holds for all 1D critical states.
