  We study a class of finite dimensional quantum dynamical semigroups exp(tL)
whose generators L are sums of Lindbladians satisfying the detailed balance
condition. Such semigroup arise in the weak coupling (van Hove) limit of
Hamiltonian dynamical systems describing open quantum systems out of
equilibrium. We prove a general entropic fluctuation theorem for this class of
semigroups by relating the cumulant generating function of entropy transport to
the spectrum of a family of deformations of the generator L. We show that,
besides the celebrated Evans-Searles symmetry, this cumulant generating
function also satisfies the translation symmetry recently discovered by
Andrieux et al., and that in the linear regime near equilibrium these two
symmetries yield Kubo's and Onsager's linear response relations.
