I hope this will further clarify matters.
It would, if it were true. But it isn't; it is objectively false as stated. The correct statement is: CLOSED Physical systems cannot produce more information at their output than was present at their input.
It is nothing more than an information theory version of the Second Law of Thermodynamics, and does not represent anything new.
Please give an example of an OPEN physical system?
Also, it has been remarked that there is no known "natural" cause of information. What do you make of a statement like that? How would you contradict it if you think it incorrect?
Must go out to tend to "elder care" this afternoon. But I'll be back later.