Fluctuation relations for diffusion that is thermally driven by a nonstationary bath

In the context of the Markovian dynamical evolution in a nonstationary thermal bath, we construct a family of fluctuation relations for the entropy production that are not verified by the work performed on the system. We exhibit fluctuation relations, which are global versions either of the generalized fluctuation-dissipation theorem around a nonequilibrium diffusion or of the usual fluctuation-dissipation theorem for energy resulting from a pulse of temperature.