"Good physicists are very wary of the perils of mixing effective theories in order to make predictions. In the absence of first principle derivations it is possible they make contradictory assumptions. This is one of the reasons why theoretical physics predictions are of no real value unless they are testable by experiment (e.g.: not inside a black hole, or an unobservable parallel universe), this isn’t just a utility judgement. Experiment is often the only way of confirming the theoretical approach, and mathematical analysis of valid systems of equations also often generate un-physical solutions along with the physical ones1 . This requires physicists to be very careful regarding what they choose to combine and conclude. Those wishing to use analogous concepts as components in a theory of data analysis should be equally wary. We cannot simply pick up formulae from a physics book and start using them as part of a data analysis because they are convenient, or even because others tell you “they work” when applied to specific data sets. It’s all too easy to generate absurd (self contradictory) ideas which defy basic logic, i.e. entertaining pseudoscience which is the analysts equivalent of time travel. In general the valid use of any mathematical theory requires justification. For example, if you think you are computing something equivalent to an entropy, what is the equivalent of ‘thermal equilibrium’ for your system? When we see people using these and other expressions outside the context of physics we should not be impressed and assume that all is well, instead we should ask ; Why? And keep asking until we get a good answer.
"[1].

[1]P.A. Bromiley, N.A. Thacker and E. Bouhova-Thacker.Shannon Entropy, Renyi Entropy, and Information