Fluctuation Relation for Qubit-Calorimetry

Motivated by proposed thermometry measurement on an open quantum system, we present a simple model of an externally driven qubit interacting with a finite sized, fermion environment acting as calorimeter. The derived dynamics is governed by a stochastic Schr\"odinger equation coupled to the temperature change of the calorimeter. We prove a fluctuation relation and deduce from it a notion of entropy production. Finally, we discuss the first and second law associated to the dynamics.