  We use a canonical quantization procedure to set up a quantum
Fokker-Planck-Kramers equation that accounts for quantum dissipation in a
thermal environment. The dissipation term is chosen to ensure that the
thermodynamic equilibrium is described by the Gibbs state. An expression for
the quantum entropy production is also provided which properly describes
quantum systems in a nonequilibrium stationary state. The time-dependent
solution is given for a quantum harmonic oscillator in contact with a heat
bath. We also obtain the stationary solution for a system of two coupled
harmonic oscillators in contact with reservoirs at distinct temperatures, from
which we obtain the entropy production and the quantum thermal conductance.
