The Shannon limit of the universe? 368 Bits?
In the paper DNA as nanotechnology: Reassessing Life's Origins through the lens of information by H Gondal
A very interesting argument style is deployed in section O to derive the universal generative capacity ceiling
What appears to be a mere probability equation is inverted into a Hartley style argument
Gondal calculates the universal phase transitions as 4.35x10¹¹⁰ by doing particles x time x reaction rate
He then deploys the 2 bits per nucleotide and basically deploys a capacity bound utilizing this formula
n = log T / log M
It yields about 184 base pairs or 368 bits as the Universal generation limit
This is actually independent of biology entirely and appears to be an upper bound of information generation in finite systems utilizing the universe as the finite system
Log 4 is H max aswell
The real interesting bit happens where a selection bias table appears to show corrected per position fidelity across the universal trial space with a curve scaling from 0.25 to 0.99995
n = log T/ - log p
This is interesting as it's directly recoverable from Shannon's formula by substituting S/N = 1-p/p
Appears to be information self reprisal
The variable P serves as a universal plugin for any conceivable model - showing to reach the minimal genome you need information specificity of 99.995% regardless of what the process is
This scaling is compared to the minimal genome by the Venter institute which is around ~1 million bits
It's not an Improbability argument but a capacity argument thus standard rebuttals such as more time or matter doesn't work as it's already been all utilized
Despite that, the table at the end showing multiple abiogenesis models hides the issue of logarithmic compression stating that you can vary trials by alot and the base pair or information limit barely moves
The simplest implication being that the universe does not have the capacity to generate life by random processes and wtv process did help serves as a information bias so strong that it's indistinguishable from pre loaded specificity
I'd appreciate some nuanced takes as this has been boggling my mind given it appears to converge with other limit theorems such as Berkenstein Bound etc