alt Hacker Newsp_i
Edit to add lots of words:
In the definition of entropy
S := -k_B sum p_i ln (p_i)
knowledge about the system enters the equation in the p_i terms.
The other term is a constant so it’s not like there are many other choices to link the entropy to the system!
Please communicate in full sentences with me.
I can only guess that your objection is something about probabilities. A microstate has a probability independent of my knowledge of the system just like the probability of having a royal flush doesn't change after drawing five cards. The probability of me ending the game with a royal flush might, but that is not what we mean by these probabilities.