  Quantum measurement is ultimately a physical process, resulting from an
interaction between the measured system and a measuring apparatus. Considering
the physical process of measurement within a thermodynamic context naturally
raises the following question: How can the work and heat be interpreted? In the
present paper we model the measurement process for an arbitrary discrete
observable as a measurement scheme. Here the system to be measured is first
unitarily coupled with an apparatus and subsequently the compound system is
objectified with respect to a pointer observable, thus producing definite
measurement outcomes. The work can therefore be interpreted as the change in
internal energy of the compound system due to the unitary coupling. By the
first law of thermodynamics, the heat is the subsequent change in internal
energy of this compound due to pointer objectification. We argue that the
apparatus serves as a stable record for the measurement outcomes only if the
pointer observable commutes with the Hamiltonian and show that such
commutativity implies that the uncertainty of heat will necessarily be
classical.
