  Quantum coherence associated with the superpositions of two different sets of
eigenbasis vectors has been regarded as essential in thermodynamics. It is
found that coherent factors can be determined by writing observables as an
expansion in the basis vectors of the systemic density operator and
Hamiltonian. We reveal the roles of coherence in finite-time thermodynamic
processes, such as the spin precession and the spontaneous emission of a
photon. Results show that the work in the spin precession and the heat in the
spontaneous emission process are mainly generated by coherence.

Quantum Physics;Statistical Mechanics