  Thermodynamics of trajectories promises to make possible the thorough
analysis of the dynamical properties of an open quantum system, a sought-after
goal in modern physics. Unfortunately, calculation of the relevant quantities
presents severe challenges. Determining the large-deviation function that gives
access to the full counting statistics associated with a dynamical order
parameter is challenging, if not impossible, even for systems evolving in a
restricted Liouville space. Acting on the realisation that the salient features
of most dynamical systems are encoded in the first few moments of the counting
statistics, in this article we present a method that gives sequential access to
these moments. Our method allows for obtaining analytical result in several
cases, as we illustrate, and allows using large deviation theory to reinterpret
certain well-known results.
