  Markovian quantum master equations (MQMEs) were established nearly half a
century ago. They have often been used in the study of irreversible
thermodynamics. However, the previous results were mainly concerned about
ensemble averages; the stochastic thermodynamics of these systems went
unnoticed for a very long time. This situation remained unchanged until a
variety of fluctuation theorems in classical and quantum regimes were found in
the past two decades. In this paper, we systematically summarize the current
understanding on the stochastic heat and work in MQMEs using two distinct
strategies. One strategy is to treat the system and its surrounding heat bath
as a closed quantum system, to suppose that the evolution of the composite
system is unitary under a time-dependent total Hamiltonian and to define the
heat and work as the changes in energy by applying two energy measurements
scheme to the composite system. The other strategy is to unravel these MQMEs
into random quantum jump trajectories (QJTs) and to define the stochastic heat
and work along the individual trajectories. Many important physical concepts,
mathematical techniques, and fluctuation theorems at different descriptive
levels are given in as detailed a manner as possible. We also use concrete
models to illustrate these results.
