  Here we clarify the assumptions made and conclusions reached in our paper
"The thermodynamical cost of some interpretations of quantum theory" [Phys.
Rev. A 94, 052127 (2016)], at the light of the criticisms of Prunkl and Timpson
[Stud. Hist. Philos. Sci. Part B 63, 114 (2018)], and Davidsson (Master thesis,
Stockholm University, 2018). We point out some misunderstandings and some
weaknesses of the counterexample Prunkl and Timpson present to challenge our
conclusion. We thus conclude, once more, that interpretations of quantum theory
which consider the probabilities of measurement outcomes to be determined by
objective properties of the measured system and satisfy the assumption that the
measured system only has finite memory have a thermodynamical cost.
