**Abstract**
Fluctuation theorems and Jarzynski equalities have attracted considerable interest, since they give equalities on physical quantities in nonequilibrium processes. On the other hand, Maxwell's demon has attracted many researchers in such diverse fields as (quantum) information theory and statistical mechanics for over one and half century. Maxwell's demon is a kind of a feedback controller who can utilize the obtained information via measurement to extract work from the system beyond the conventional second law.

In this seminar, we consider quantum fluctuation theorems under measurement and feedback control by taking into accout the information gain, which correctly characterizes the acquired knoledge of the system due to the measurement. The obtained equalities repsoduce the second law of thermodynamics under measurement and feedback control.

[1] Ken Funo, Yu Watanabe, and Masahito Ueda, Phys. Rev. E 88, 052121 (2013)