Fig. 1

Schematic of the experimental setup. a Heat flows from the hot to the cold spin (at thermal contact) when both are initially uncorrelated. This corresponds to standard thermodynamic. For initially quantum-correlated spins, heat is spontaneously transferred from the cold to the hot spin. The direction of heat flow is here reversed. b View of the magnetometer used in our NMR experiment. A superconducting magnet, producing a high-intensity magnetic field (B₀) in the longitudinal direction, is immersed in a thermally shielded vessel in liquid He, surrounded by liquid N in another vacuum separated chamber. The sample is placed at the center of the magnet within the radio-frequency coil of the probe head inside a 5-mm glass tube. c Experimental pulse sequence for the partial thermalization process. The blue (black) circle represents x (y) rotations by the indicated angle. The orange connections represents a free evolution under the scalar coupling, \({\cal{H}}_{\mathrm{J}}^{{\mathrm{HC}}} = (\pi \hbar /2)J\sigma _z^{\mathrm{H}}\sigma _z^{\mathrm{C}}\), between the ¹H and ¹³C nuclear spins during the time indicated above the symbol. We have performed 22 samplings of the interaction time τ in the interval 0 to 2.32 ms