 Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem.From this viewpoint, the measurement process is regarded as a process where the correlation (mutual information) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases.If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied.