  In this thesis, we considered quantum systems coupled to several baths. We
supposed that the system state is governed by the quantum master equation
(QME). We investigated the quantum pump and the excess entropy production. In
the first half of the thesis, we investigated the quantum pump using the full
counting statistics with quantum master equation (FCS-QME) approach. In the
latter part of the thesis, we investigated the excess entropy production. The
average entropy production is composed of the time integral of the
instantaneous steady entropy production rate and the excess entropy production.
We define average entropy production rate using the average energy and particle
currents, which are calculated by using the full counting statistics with QME.
The excess entropy production is given by a line integral in the control
parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN)
vector. In the weakly nonequilibrium regime, we show that BSN vector is
described by $\ln \rho_0^{(-1)}$ and $\rho_0$ where $\rho_0$ is the
instantaneous steady state of the QME and $\rho_0^{(-1)}$ is that of the QME
which is given by reversing the sign of the Lamb shift term. In general, the
potential dose not exist. The origins of the non-existence of the potential are
a quantum effect (the Lamb shift) and the breaking of the time-reversal
symmetry. The non-existence of the potential means that the excess entropy
essentially depends on the path of the modulation. If the system Hamiltonian is
non-degenerate or the Lamb shift term is negligible, the excess entropy
production approximately reduces to the difference between the von Neumann
entropies of the system. We pointed out that the expression of the entropy
production obtained in the classical Markov jump process is different from our
result and showed that these are approximately equivalent only in the weakly
nonequilibrium regime.
