  Fluctuation theorems are fundamental extensions of the second law of
thermodynamics for small systems. Their general validity arbitrarily far from
equilibrium makes them invaluable in nonequilibrium physics. So far,
experimental studies of quantum fluctuation relations do not account for
quantum correlations and quantum coherence, two essential quantum properties.
We here experimentally verify detailed and integral fully quantum fluctuation
theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a
nuclear magnetic resonance setup. We confirm, in particular, individual
integral fluctuation relations for quantum correlations and quantum coherence,
as well as for the sum of all quantum contributions. These refined formulations
of the second law are important for the investigation of fully quantum features
in nonequilibrium thermodynamics.
