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Heat and work in Markovian quantum master equations: concepts,
uctuation theorems, and computations
Liu Fei
2018, 38 (1):
1-63.
PDF (1047KB)
(
459
)
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 physical important 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.
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