Negative entropy

[andresilvapimentel]

I performed the calculation of the entropy of a protein region (five aminoacids). It turns out negative number in the entropy array. What does it mean?

[jokr91]

Hi Andre,

this is not really a big issue, the values for the dihedral entropy range from negative infinity (only one state) to R * ln(2 pi) (all states are equally likely).
It is more interesting to compare the values between different parts in the molecule or between different molecules.

[andresilvapimentel]

Thanks. But I did not quite understand your explanation.

I calculated the dihedral entropy of the region of a nornal protein (5 aminoacids) by using the code:
S = dih_ent.entropy
The result was: array([ 1.02632743, 0.27675774, 5.29546661, -2.06808451, 3.92356854,
-1.25778001, -0.2144733 , 9.55031112, 1.43636179, 6.05720575])

Then, I calculated the dihedral entropy of the region of a mutated protein (5 aminoacids) by using the same code:
The result was: array([-0.85348536, -1.25256182, -2.80944595, -0.0278988 , -0.68257193,
-1.39297199, 0.484963 , -1.88314858])

How do I compare these two entropies? I emphasize that I still think the negative entopies are too weird and make no sense physically!!!

[Clownshift]

In case other users stumble upon the question:
"Can entropy be negative?"

We do not want to address this question here in detail, as it is (at least in our eyes) not actually related to our implementation. However, we want to point out that from the mathematical definition of entropy (according to, e.g., Shannon), it may very well be negative. For example for very narrow probability distributions.