I’ve written before about Rényi entropy *H*_{q} and most recently *q*-log entropy *S*_{q}, two generalizations of Shannon entropy.

There are simple equations relating Rényi entropy and *q*-log entropy if we measure both in nats:

I mentioned in the post on *q*-log entropy that there were two possible ways it could be defined. The equation above applies to what I called in that post *S*_{q}, not *S *‘_{q}. In other words, it applies to the version that uses ln_{q}(1/*p*) and not the version that uses −ln_{q}(*p*). Recall that these are not equal unless *q* equals 1. When *q* does equal 1, then Rényi entropy and *q*-log entropy are the same as Shannon entropy.

Source: Tom Leinster, Entropy and Diversity: The Axiomatic Approach.