  For a bipartite state with equal local dimension d, we prove that one can
obtain work gain under Landauer's erasure process on one party in identically
and independently distributed (iid) limit when the corresponding fully
entangled fraction is larger than 1/d. By processing a given state to the
maximally mixed state, we give an approximation for the largest extractable
work with an error in the energy scale, which becomes negligible in the large
system limit. As a step to link quantum thermodynamics and quantum nonlocality,
we also provide a simple picture to approximate the optimal work extraction and
suggest a potential thermodynamic interpretation of fully entangled fraction
for isotropic states.
