  Measuring the thermodynamic properties of open quantum systems poses a major
challenge. A calorimetric detection has been proposed as a feasible
experimental scheme to measure work and fluctuation relations in open quantum
systems. However, the detection requires a finite size for the environment,
which influences the system dynamics. This process cannot be modeled with the
standard stochastic approaches. We develop a quantum jump model suitable for
systems coupled to a finite-size environment. With the method we study the
common fluctuation relations and prove that they are satisfied.
