I had two options: Not even mentioning it, or try to go and fix it. I opted for the first as I had no idea of how to fix it, but I felt I was hiding a big issue with the theory under the carpet, so one random day I tried to find a fix.
Ideally, I thought, I would only need to replace the (pi × log(pi)) part with something like (pipi), but it was such a naive idea I almost gave up before having a look, but I did: how different do those two functions looks like when plotted on their domain interval (0, 1)?
So my first attempt to build a new entropy was this:
After trying to find the quadrature of the circle for some time, I realised I only reverted part of the logarithmic problem: the summary 𝚺 sign should had been replaced with the original multiplication one, ∏. The entropy I was looking for was a multiplication of terms, not a summary as usually expected.