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In this thesis, we considered quantum systems coupled to several baths. Wesupposed that the system state is governed by the quantum master equation(QME). We investigated the quantum pump and the excess entropy production. Inthe first half of the thesis, we investigated the quantum pump using the fullcounting statistics with quantum master equation (FCS-QME) approach. In thelatter part of the thesis, we investigated the excess entropy production. Theaverage entropy production is composed of the time integral of theinstantaneous steady entropy production rate and the excess entropy production.We define average entropy production rate using the average energy and particlecurrents, which are calculated by using the full counting statistics with QME.The excess entropy production is given by a line integral in the controlparameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN)vector. In the weakly nonequilibrium regime, we show that BSN vector isdescribed by $\ln \rho_0^{(-1)}$ and $\rho_0$ where $\rho_0$ is theinstantaneous steady state of the QME and $\rho_0^{(-1)}$ is that of the QMEwhich is given by reversing the sign of the Lamb shift term. In general, thepotential dose not exist. The origins of the non-existence of the potential area quantum effect (the Lamb shift) and the breaking of the time-reversalsymmetry. The non-existence of the potential means that the excess entropyessentially depends on the path of the modulation. If the system Hamiltonian isnon-degenerate or the Lamb shift term is negligible, the excess entropyproduction approximately reduces to the difference between the von Neumannentropies of the system. We pointed out that the expression of the entropyproduction obtained in the classical Markov jump process is different from ourresult and showed that these are approximately equivalent only in the weaklynonequilibrium regime.

Theoretical studies on quantum pump and excess entropy production: Quantum master equation approach