title: Quantum fluctuation theorems and generalized measurements during the force protocol.
abstract: Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function conditioned on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed fluctuation theorems with an arbitrary number of intervening measurements are obtained.
authors.affiliation: Asia Pacific Center for Theoretical Physics (APCTP), San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea and Department of Physics, POSTECH, San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea.
authors.forename: Gentaro
authors.initials: G
authors.lastname: Watanabe
authors.affiliation: Asia Pacific Center for Theoretical Physics (APCTP), San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea.
authors.forename: B Prasanna
authors.initials: BP
authors.lastname: Venkatesh
authors.affiliation: Asia Pacific Center for Theoretical Physics (APCTP), San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Korea and Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Talkner
authors.affiliation: Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany.
authors.forename: Michele
authors.initials: M
authors.lastname: Campisi
authors.affiliation: Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany and Nanosystems Initiative Munich, Schellingstraße 4, D-80799 München, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Hänggi