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Fluctuation theorems in presence of information gain and feedback

In this study, we rederive the fluctuation theorems in presence of feedback, by assuming the known Jarzynski equality and detailed fluctuation theorems. We first reproduce the already known work theorems for a classical system, and then extend the treatment to the other classical theorems. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system-bath coupling. However, it is assumed that the measurement process involves classical errors.