Computers, landauer limit, future computation and the brain

About 2 years ago computers were about a factor of 100-10,000 from the landauer limit.
 "However, current computers operate at only 100-10,000 times this limit, forming an argument
that historical rates of efficiency scaling must soon slow. "-(2016)A Path Toward Ultra-Low-Energy Computing -source

Yet efficiency continues to increase, research in the lab is testing designs that could go very near the landauer limit.  Such computers, as I've stated previously, will be here within decades at most.

Unless the brain uses exotic physics it is very unlikely to escape this limit, thus the nature of its function would be computational, and there would be severe limit on the number of computations performed.  It is said the brain uses only 20W, but some have suggested only about 10W goes directly towards computation.    This suggests that if we take the higher pessimistic estimate and pessimistically assume the brain operates at the exact landauer limit(it may be near but probably does not exactly reach it), it may be that it performs 10,000 times the amount of computation as a 10W computer of today's highest efficiency.

Yet within the near future, we will have computers that approach the landauer limit, but have 1000+W available. and in institutions Megawatt+ available.

Koomey's law describes a long-term trend in the history of computing hardware. The number of computations per joule of energy dissipated has been doubling approximately every 1.57 years. -wiki

Comment on Human brain computational capacity vs near future computers near landauer limit

 When people calculate the computing power of the human brain they sometimes multiply number of synapses per neuron(often an overestimate), by maximum possible activity rates(again something that is only sustained by a neuron usually for short periods), by number of neurons(and again often another overestimate). This is a ridiculous calculation, when you consider that at least in the neocortex, the most relevant part, it is only a few percent of total neurons that are active for a given chunk of tissue. It is the only way you get the human brain performing ridiculously more computations on 20W than the theoretical numbers hypothesized for future computers near the landauer limit and consuming 100+W.

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment"-Wikipedia

For example take this

"A common approach for estimating the computational complexity of the brain is to assume all information processing in the brain can be represented by the combination of impulses when a neuron fires (action potentials) and the size (mostly number of receptors) of the synapses that each neuron has. Thus one can multiply the estimates for the number of neurons and their synapses and add everything together. Then one multiplies this by the rate of fire for the average neurons which is about 200 action potentials per second.... So my estimate would be 1.075×10^21 FLOPS for the brain..."- timdettmers brain-vs-deep-learning-singularity 

The brain is estimated to consume 20W in total energy, some have said about 50~% of this probably goes to other non information processing functions, allowing only 10W to remain for computation.   Now that amount of computation cannot be at rates beyond the physical limits for conventional processes.

It was said by some sources computers some years ago were within 10000~ factor of the landauer limit.   Today they must be closer as computers have increased substantially, several fold, in energy efficiency.   But still a modern gpu consumes about 150W~ per 10 Teraflops.   Even taking the 10000 factor which no longer applies, some have said it is now less than 5,000 factor over landauer limit, that would mean at landauer limit 150W future computer would perform 50Petaflops at room temperature.  It is conceivable within 1-2 decades such landauer limit computers will be out of the labs and in the market.

Yet as we've said some estimates give the brain just 10Watts for computation.   So an estimate of 10^21 FLOPs which is substantially higher is basically impossible barring exotic architectures, such as ones using reversible computing, which it seems the brain does not use.