There is a relation but it is not too important in practice, which you'd find if you'd attempt to read what you avoided... twice.
The theoretical information change limits are theoretical, in practice, there's always significantly more energy used, so 'pizza didn't even have to mention that limit in this case (although knowing that the limits exists is also important in considering what is possible and what simply is not).
The wikipedia article you ignored shows that in the formula T is temperature in Kelvins, i.e. 310 K for a body temperature, and k is of order 1-e28. You get some small energy, log 2 is not relevant for the order of magnitude. Then you need to use time to get just the power in Watts, and which time should you use? Even looking at extreme processes: does killing somebody "erase" all the memory at once? Certainly not, as the processes in the brain are much more complex.... but the destruction of just a pieces of a brain makes it not functioning at all, like all complex systems, etc. And it the end it would be still not much relevant to hang to the formula for any known system, either developed by evolution or by humans.
Also once you google the name of the limit you get a lot of articles, not just the one in Wikipedia. Ditto for the brain power usage.