Great. I’m glad we are on the same page on the definition of KL then.
Because KL is always positive, this forces several major changes to your understanding. You had thought that (in your toy case of P53), that cancer was an information loss. This is false. It requires a positive amount of information greater than zero, functional information, to move from the normal state to the new function of a cancer state.
That means cancer is gaining functional information. What remains is merely to compute how much.
I disagree. This has to do with the fact that you’ve only worked out the math assuming that KL = delta H. Now you realize this not the case, you have rework out the math. It turns out that the true amount of information is much more. This mathematical error we just caught has a massive ripple effect on all the calculations.
Yes, but this “incorrect way” is precisely how you measure the function of protein families. So behooves us to compute the information content of carcinogenic p53 in a way that precisely mirrors your paper until you are ready to concede your paper is in error. “Normal” p53 does not have the cancer function, but “carcinogenic” p53 does. In your paper, you would compute the FSC of the “carcinogenic” p53 in relation to a MaxEnt prior, ignoring the non-function “normal” p53. So that is what we should do here.
Unless you want to concede now that FSC is an erroneous way of computing FI. That is precisely where this is headed. The sooner we get there the better. I’m already there. Are you? Or do we need to play this out?