A Boltzmann brain is a hypothesized self-aware entity that arises due to random fluctuations in the quantum vacuum. Does Islamic theology allow for this interpretation of Allah?
The Boltzmann brain is a
...self-aware entity that arises due to random fluctuations out of a state of chaos (Wikipedia),
which implies that, if a Boltzmann brain exists, it's most probably among the most rudimentary of brains, as creating more sophisticated brains is far less probable. This is not compatible with our understanding of Allah, e.g. being all-knowing.
And it's also inconsistent with the Qur'an:
He is the First and the Last, the Ascendant and the Intimate, and He is, of all things, Knowing. -- Qur'an 57:3
We don't believe in a model of the universe without Allah, and a Boltzmann brain requires things to exist before it's spontaneously created.