Generalized detailed fluctuation theorem under nonequilibrium feedback control

It has been shown recently that the Jarzynski equality is generalized under nonequilibrium feedback control T. Sagawa and M. Ueda, Phys. Rev. Lett. 104, 090602 (2010). The presence of feedback control in physical systems should modify both the Jarzynski equality and the detailed fluctuation theorem K. H. Kim and H. Qian, Phys. Rev. E 75, 022102 (2007). However, the generalized Jarzynski equality under forward feedback control has been proved by considering that the physical systems under feedback control should locally satisfy the detailed fluctuation theorem. We use the same formalism and derive the generalized detailed fluctuation theorem for nonequilibrium driven systems under feedback control. We find that the feedback control in a physical system should preserve the detailed fluctuation theorem if the system has the same feedback information measure in forward and reverse directions.