Constructing Formula of Nonequilibrium Physics by using Quantum Continuous Measurement and Quantum Field Theory

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We derive integral quantum fluctuation theorems and quantum Jarzynski equalities for a feedback-controlled system and a memory which registers outcomes of the measurement. The generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities. We also show that entanglement can be utilized to extract the thermodynamic work beyond classical correlation via feedback control. We propose new hypothesis for thermalization of isolated quantum systems, and show the hypothesis gives larger contribution than well known hypothesis to the thermalization. We also show that the system thermalize even if it is integrable.We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. A formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived, which quantitatively describes the measurement backaction of photon-counting on the homodyne output.