  We show that for the Lindblad evolution defined using (at most) quadratically
growing classical Hamiltonians and (at most) linearly growing classical jump
functions (quantized into jump operators assumed to satisfy certain ellipticity
conditions and modeling interaction with a larger system), the evolution of a
quantum observable remains close to the classical Fokker--Planck evolution in
the Hilbert--Schmidt norm for times vastly exceeding the Ehrenfest time (the
limit of such agreement with no jump operators). The time scale is the same as
in the recent papers by Hern\'andez--Ranard--Riedel but the statement and
methods are different. The appendix presents numerical experiments illustrating
the classical/quantum correspondence in Lindblad evolution and comparing it to
the mathematical results.
