Repeated temperature measurements in quantum thermodynamics

In this work, we model the temperature measurement as a transformation of the arbitrary state into the Gibbs state. We start with a general formalism of ansatz-posteriors, which includes many usual models of posterior states due to measurement or state preparation. On the one hand, it contains models of selective and non-selective measurements posteriors as special cases, which allows us to consider it as a generalization of usual measurement models. On the other hand, it contains the above mentioned transformation into the Gibbs state as a special case as well. We derive an analogue of the master equation in the stroboscopic limit of repeated measurements. Then we apply our general approach to temperature measurement.