  We obtain a non-Markovian quantum master equation directly from the
quantization of a non-Markovian Fokker-Planck equation describing the Brownian
motion of a particle immersed in a generic environment (e.g. a non-thermal
fluid). As far as the especial case of a heat bath comprising of quantum
harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett
master equation on the basis of which we work out the concept of
non-equilibrium quantum thermal force exerted by the harmonic heat bath upon
the Brownian motion of free particle. The classical limit (or dequantization
process) of this sort of non-equilibrium quantum effect is scrutinized, as
well.
