![]() ![]() We study processes in a time interval of few milliseconds, which is much shorter than any relevant decoherence time of the system (of the order of few seconds) 26. The sample is placed inside a superconducting magnet that produces a longitudinal static magnetic field (along the positive z-axis) and the system is manipulated by time-modulated transverse radio-frequency (rf) fields. In our investigation, we consider two nuclear spins-1/2, in the 13C and 1H nuclei of a 13C-labeled CHCl 3 liquid sample diluted in Acetone-d6 (Fig. ![]() It has for this reason become a premier tool for the study of quantum thermodynamics 7, 26, 27. NMR offers an exceptional degree of preparation, control, and measurement of coupled nuclear spin systems 21, 22. We finally theoretically derive and experimentally investigate an expression for the heat current that reveals the trade off between information and entropy. We further establish the nonclassicallity of the initial correlation by evaluating its nonzero geometric quantum discord, a measure of quantumness 24, 25. However, the standard second law in its local form apparently fails to apply to this situation with initial quantum correlations. The second law for the isolated two-spin system is therefore verified. For initially correlated systems, we observe a spontaneous heat current from the cold to the hot spin and show that this process is made possible by a decrease of their mutual information. We experimentally determine the energy change of each spin and the variation of their mutual information 23. Allowing thermal contact between the qubits, we track the evolution of the global state with the help of quantum-state tomography 21. ![]() Here, we report the experimental demonstration of the reversal of heat flow for two initially quantum-correlated qubits (two-spin-1/2 systems) prepared in local thermal states at different effective temperatures employing Nuclear Magnetic Resonance (NMR) techniques 21, 22. This phenomenon has been predicted to occur in general multidimensional bipartite systems 9, 10, including the limiting case of two simple qubits 10, as well as in multipartite systems 11. ![]() However, it has been theoretically suggested that for quantum-correlated local thermal states, heat might flow from the cold to the hot system, thus effectively reversing its direction 9, 10, 11, 12. As a result, according to the second law, heat will flow from the hot object to the cold object. In standard thermodynamics, systems are assumed to be uncorrelated before thermal contact. This opens the possibility to control or even reverse the direction of heat flow, depending on the initial conditions. The observation of the average positivity of the entropy production in nature is often explained by the low entropy value of the initial state 3. Initial conditions not only induce irreversible heat flow, they also determine the direction of the heat current. It has in particular been shown that a preferred direction of average behavior may be discerned, irrespective of the size of the system 20. These experiments have been accompanied by a surge of theoretical studies on classical and quantum irreversibility 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Quantitative experimental confirmation of this conjecture has recently been obtained for a driven classical Brownian particle and for an electrical RC circuit 6, as well as for a driven quantum spin 7, and a driven quantum dot 8. On the other hand, Boltzmann related it to specific initial conditions of the microscopic dynamics 3, 4, 5. At a phenomenological level, the second law of thermodynamics associates such irreversible behavior with a nonnegative mean entropy production 2. According to Clausius, heat spontaneously flows from a hot body to a cold body 1. ![]()
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