This question is inspired by the following example given in Barnett's book on quantum information:
(PDF here, starting at the bottom of page 5)
I am not a physicist, but I'll accept that the calculation of the increase in physical entropy associated with this procedure is correct. My confusion is about how the second law of thermodynamics can be saved by claiming that the process of measuring the position of the molecule produces an entropy of at least $k_B\ln2$.
My question is: Why can we just assume that "entropy" of information is comparable with physical entropy? The best explanation that I've been able to find is that they're defined in similar ways and satisfy the same basic properties. This seems no different from saying "decibels and earthquake intensity are both measured logarithmically and are therefore comparable", which of course makes no sense.
As I said above, my only physics background is a first-year course, so I'd appreciate if answers could try to be accessible to someone who hasn't done thermodynamics...