>>16743567
I'm kind of shit posting before but to take your point as you're making it I think we can skip your argument about entropy increasing meaning new information is being introduced and without access ahead of time to that new info future states cannot be calculated because a simpler argument makes your case and that goes like this
to know the state means you've made a measurement
making a measurement is a synonym for causing a collision with whatever part of the system you are measuring
collisions affect the thing measured
thus in principle determinism is impossible from within the system because you have to disturb it with measurement in order to know the state