  We present a general method to undertake a thorough analysis of the
thermodynamics of the quantum jump trajectories followed by an arbitrary
quantum harmonic network undergoing linear and bilinear dynamics. The approach
is based on the phase-space representation of the state of a harmonic network.
The large deviation function associated with this system encodes the full
counting statistics of exchange and also allows one to deduce for fluctuation
theorems obeyed by the dynamics. We illustrate the method showing the validity
of a local fluctuation theorem about the exchange of excitations between a
restricted part of the environment (i.e., a local bath) and a harmonic network
coupled with different schemes.
