Bremermann's limit vs Planck frequency

Question

Bremermann's limit, as maximum possible computation power or CPU total computing frequency, is known to be on the order $10^{50}~text{Hz}/text{kg}$.
Why max computation frequency for unit mass can exceed Plank frequency, which is on the order of $10^{43} ~text{Hz}$ and how it is related to it?

user253751 · Accepted Answer

It's bits per second. It's not a frequency. It could be 1 bit being processed $10^{50}$ times per second, which would be faster than the Planck frequency, but it could also be $10^{50}$ bits being processed once per second each, which wouldn't.
You're also comparing things with different units. It's like saying that the Schwarzschild constant (mass of a black hole compared to its radius) is $1.34663531 × 10^{27} kg / m$, but the observable universe has a mass of $1.5×10^{53} kg$, so why isn't the observable universe a black hole? Well, the observable universe has a radius of more than 1 metre. Or, the speed limit is only 50 mph, so how can you drive from from New York to Philadelphia (94.5 miles)? Well, it takes more than one hour.
If you were going to choose an arbitrary amount of mass to put into the equation, there's no reason it would have to be 1kg. A more "natural" amount of mass would be something like the Planck mass or the electron mass. (very different amounts of mass, by the way). If the speed limit did somehow dictate how far you could travel, it would be more logical to multiply it by the Planck time, than by 1 hour - and by that reasoning your car couldn't even drive a millimetre, which shows how that reasoning is completely wrong.

Agnius Vasiliauskas · Answer

Maybe I have not expressed my question in a good way. The core thing which I was interested in was,- Can a Bremermann's limit be calculated using only Plank units or at least approximated by it ?
Thanks to @user253751, I can now understand that. Usually maximum possible bit-rate is achieved by equating quanta energy to $mc^2$ :
$$mc^2 = hf $$,
then maximum bit-rate possible per unit mass is :
$$R_b = frac fm = frac {c^2}{h}$$
which is $1.3 times 10^{,50} ~text{bps}/text{kg}$, here "bps" means bits-per-second. Now, technically bit-rate has dimensions of $text{Hz/kg}$, so one can approximate maximum bit-rate using Plank frequency and Plank mass :
$$ R_b = frac{f_{_P}}{m_{_P}} $$
Using these we get $R_b$ also on the order $10^{50}$ bps/kg ! So conclusion is that bit-rate maximum limit can be quite accurately modeled using Plank units only.

Bremermann's limit vs Planck frequency

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