Rodríguez-Rosario, César A.Frauenheim, ThomasAspuru-Guzik, Alan2015-07-232013Rodríguez-Rosario, César A., Thomas Frauenheim, and Alán Aspuru-Guzik. 2013. "Thermodynamics of quantum coherence." Working paper, Harvard University, August 6, 2013.http://nrs.harvard.edu/urn-3:HUL.InstRepos:17578537Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources [1]. Quantum coherences seem to be a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines [2, 3], affect the efficiency of quantum transport [4{6], lead to violations of Fourier's law [7], and can be used to dynamically control the temperature of a state [8]. However, the role of quantum coherence in thermodynamics [9] is not fully understood. Here we show that the relative entropy of a state with quantum coherence with respect to its decohered state captures its deviation from thermodynamic equilibrium. As a result, changes in quantum coherence can lead to a heat ow with no associated temperature, and a ffect the entropy production rate [10]. From this, we derive a quantum version of the Onsager reciprocal relations [11] that shows that there is a reciprocal relation between thermodynamic forces from coherence and quantum transport. Quantum decoherence can be useful and offers new possibilities of thermodynamic control for quantum transport.en-USQuantum Physics (quant-ph)Statistical Mechanics (cond-mat.stat-mech)Research Paper or Report2015-07-23