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

Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks