Probability theory is fundamental. Outside of the quantum stuff it's some strange macro phenomena that occurs almost separate from physics.
It's strange, I'm no physicist but at the atomic level it seems particles are fundamentally probabilistic. But then even at a macro level completely separate from the underlying physics something like rolling dice will obey the laws of physics but also at a higher macro level it converges on following the laws of probability.
It's also connected with knowledge. I dunno... it's weird, when I think deeply about probability and why it works I get confused. It started with an interest in entropy as this weird macro law that somehow lives separate from physics, but then I realized entropy is just a consequence of probability.
Maybe probability is like logic. Something completely axiomatic. Eh I'm just rambling now.
Speaking as a physicist, I think you're basically on the right track! (But also, this is as much philosophy of math/science as it is physics, so I wouldn't quite call myself an authority on this.)
I definitely think of probability as something like a mental framework with a set of axioms that can be applied to anything where the axioms fit well enough, which can be "true" quantum probability or sequential frequentist dice rolls or subjective Bayesian stuff.
Time always increases.
Entropy always increases.
Entropy is disorder.
Disorder means incompressible information.
True Randomness provides incompressible information.
This implies randomness is being injected into the universe.
So injecting randomness is the reason why time increases.
The above is the gestalt formed in my mind after listening to lot of pop physics lectures. Probability distributions from which fundamental particles choose their values are like ways to introduce controlled randomness into the system.
The link to "more is different" provides an opposite claim: it demonstrates a system without emergent properties, but is reducible alright, so it's not an argument against reducibility.
It's strange, I'm no physicist but at the atomic level it seems particles are fundamentally probabilistic. But then even at a macro level completely separate from the underlying physics something like rolling dice will obey the laws of physics but also at a higher macro level it converges on following the laws of probability.
It's also connected with knowledge. I dunno... it's weird, when I think deeply about probability and why it works I get confused. It started with an interest in entropy as this weird macro law that somehow lives separate from physics, but then I realized entropy is just a consequence of probability.
Maybe probability is like logic. Something completely axiomatic. Eh I'm just rambling now.