  We demonstrate the validity of the current fluctuation theorem for a double
quantum dot surrounded by four terminals within the Born-, Markov- and secular
approximations beyond the Coulomb-blockade regime. The electronic tunneling to
two fermionic contacts conserves the total number of electrons, and the
internal tunneling is phonon-assisted by two bosonic baths. Adapted choice of
thermodynamic parameters between the baths may drive a current against an
existing electric or thermal gradient. We study the apparent violation of the
fluctuation theorem when only some of the energy and matter currents are
monitored.
