  We study the modification of the second law of thermodynamics for a quantum
system interacting with a reservoir regarding quantum coherence. The whole
system is isolated so that neither energy nor information is lost. It is
discovered that the coherence of the reservoir can serves as a useful resource
allowing the system extract more energy from the reservoir; among the coherence
measures, only is the relative entropy of coherence feasible to quantitatively
characterize energy exchange. We demonstrate that a thermodynamic cycle between
two coherent reservoirs can output more work than its classical counterpart.
The efficiency of such cycle surpasses the Carnot efficiency, which is the
upper bound of heat engine efficiency in classical regime.
