We extend the Exchange Fluctuation Theorem for energy exchange between
thermal quantum systems beyond the assumption of molecular chaos, and describe
the non-equilibrium exchange dynamics of correlated quantum states. The
relation quantifies how the tendency for systems to equilibrate is modified in
high-correlation environments. Our results elucidate the role of measurement
disturbance for such scenarios. We show a simple application by finding a
semi-classical maximum work theorem in the presence of correlations.