Of course the brain uses quantum mechanics, it exists in the real world. What has yet to be demonstrated is any link to consciousness.
How would quantum theory explain the thermodynamics of increased mental clarity reported by humans on 3-5 day of fasting induced ketosis? Or multiple biocomputational benefits of mTOR inhibition (by e.g. rapamycin for longevity purposes), reduced rate of metabolism?
Extrapolating to modern mechanotech, this would be similar to an airplane flying faster and better upon regular reduction of fuel to it. Imagine a computer running more loads and faster upon regular reduction of AC power to it. Thus linear application of thermodynamics seems rather ridiculous and quantum theory may not save, because it disintegrates beyond the Plank's scale.
ps: not that I like all of Levin's work, I do admit that his tendency to abstract into grand ideas is not helping, but I think the morphogenesis/gap-junctions part of his work is still very interesting and straightforward.
While with fasting it is a reduction of actual food/fuel. Garbage collection can be comparable to fasting-induced autophagy, but in fasting it is also an absence of growth signals like IGF-1 that provides gains in health function (though Greg Fahy research on thymus regeneration in humans with a mix including a growth hormone may contradict this).
The majority of Levin's work in developmental biology done in embryos, which are naturally a highly flexible tissue and naturally express high levels of Yamanaka genes, which are now used for epigenetic reprogramming (OSK). Growing eyes on the tadpole's tail is cool, but I want to grow a tooth for myself now.
In a recent podcast #300 Attia was again mentioning the rather reliable benefits of caloric restriction. So thermodynamically it still seems ridiculous that by reducing the inflow of energy (at least the one of the most well-known type) the biological (and presumable computational) efficiency is increased at literally no cost.