  The relation between the work performed to a system and the change of its
free energy during a certain process is important in nonequilibrium statistical
mechanics. In particular, the work relation with measurement and feedback
control has attracted much attention, because it resolved the paradox
concerning Maxwell's demon. Most studies, however, assume that their target
systems are isolated or isothermal. In this paper, by considering a
nonisothermal system, we generalize the Sagawa-Ueda-Jarzynski relation, which
involves measurement and feedback control, and apply it to a realistic model.
Furthermore, when the temperature profile is quadratic, we see that the system
is governed by Tsallis statistical mechanics. In addition, we show that our
formulation provides the generalized version of the second law of information
thermodynamics and a set of work relations for isothermal systems.
