I have already parse other posts about this subject but none of them seems to answer completely to my interogation
[ this interrogation is to put in relation with this question Is there an equivalence between information, energy and matter? ]
indeed according to Bekenstein
the thermodynamic entropy and Shannon entropy are conceptually equivalent.
the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information that would be needed to implement any particular arrangement ...
...of matter and energy
for some, thermodynamic entropy can be seen as a specific instance of Shannon entropy. In short, the thermodynamic entropy is a Shannon entropy, but not necessarily vice versa.
for others, Shannon entropy is a mathematical quantity on ""abstract systems"" and have nothing to do with thermodynamics entropy.
so is there a consensual responce to that question:
Is there an equivalence between Boltzmann entropy and Shannon entropy..?