@Jarzynski2; @Kurchan; @Tasaki2; @Hatano; @Evans2; @Cohen; @Jarzynski3; @Jarzynski4; @Harada; @Seifert2; @EspositoQ; @Gaspard; @Saito; @Ohkuma; @Kawai; @Marin; @Nakagawa1; @Nakagawa2; @Utsumi; @HanggiQ; @Ren; @Hasegawa; @Esposito; @HanggiQ2; @Vaikuntanathan] have recently been found. On the other hand, experimental techniques have been developed to manipulate and observe small thermodynamic systems such as macromolecules and colloidal particles, and several nonequilibrium equalities have been experimentally verified [@Wang; @Liphardt; @Trepagnier; @Carberry; @Collin; @Douarche; @Andrieux1; @Toyabe1; @Toyabe2; @Hayashi; @Nakamura]. Moreover, artificial [@Serreli; @Rahav; @Kay; @H] and biological [@Schliwa] molecular machines have been investigated. In these contexts, feedback control is useful to realize intended dynamical properties of small thermodynamic systems, and it has become a topic of active research [@Cao1; @Kim; @Lopez; @Cao2; @Cao3; @Bonaldi; @Suzuki1; @Sagawa-Ueda3; @Suzuki2; @Brandes; @Ponmurugan; @Horowitz; @Morikuni; @Seifert3; @Horowitz2; @Esposito2; @Vaikuntanathan2; @Sagawa; @Lahiri; @Horowitz3; @Pekola; @Toyabe3]. Secondly, feedback control sheds light on the foundations of thermodynamics and statistical mechanics concerning “Maxwell’s demon” [@Maxwell; @Demon; @Szilard; @Brillouin; @Bennett; @Landauer]. In fact, Maxwell’s demon performs measurement and feedback control on thermodynamic systems. Recently, Maxwell’s demon has attracted renewed interest [@Lloyd1; @Lloyd2; @Lloyd3; @Touchette; @Zurek; @Scully; @Kieu; @Allahverdyan; @Quan; @Nielsen; @Sagawa-Ueda1; @Jacobs; @Sagawa-Ueda2; @Maruyama; @SWKim] from the standpoints of modern information theory and statistical mechanics.

A quintessential model 