I think you’re probably right. It does seem plausible that there is some subtle structure which is preserved after 20 seconds, such that the resulting distribution over states is feasibly distinguishable from a random configuration, but I don’t think we have any reason to think that this structure would be strongly correlated with which side of the box contains the majority of particles.
The variance in density will by-default be very low, so the effect size of such structure really doesn’t have to be very high. Also, if you can identify multiple such structures which are uncorrelated, you can quickly bootstrap to relatively high confidence.
I don’t think “strong correlation” is required. I think you just need a few independent pieces of evidence. Determining such independence is usually really hard to establish, but we are dealing with logical omniscience here.
For example, any set of remotely coherent waves that form in the box with non-negligible magnitude would probably be enough to make a confident prediction. I do think that specific thing is kind of unlikely in a totally randomly initialized box of gas, but I am not confident, and there are many other wave-like patterns that you would find.
I think you’re probably right. It does seem plausible that there is some subtle structure which is preserved after 20 seconds, such that the resulting distribution over states is feasibly distinguishable from a random configuration, but I don’t think we have any reason to think that this structure would be strongly correlated with which side of the box contains the majority of particles.
The variance in density will by-default be very low, so the effect size of such structure really doesn’t have to be very high. Also, if you can identify multiple such structures which are uncorrelated, you can quickly bootstrap to relatively high confidence.
I don’t think “strong correlation” is required. I think you just need a few independent pieces of evidence. Determining such independence is usually really hard to establish, but we are dealing with logical omniscience here.
For example, any set of remotely coherent waves that form in the box with non-negligible magnitude would probably be enough to make a confident prediction. I do think that specific thing is kind of unlikely in a totally randomly initialized box of gas, but I am not confident, and there are many other wave-like patterns that you would find.