Does this question, as posed, admit the possibility that the answer could be “it depends on what the initial random configuration is”? I suspect that’s what it is: there are states that robustly result in the left side having more particles than the right after 20s.
The bet would then be over the integral of all the random initializations (and random perturbations). I.e. does a random initializations in-expectation leave enough information intact for 20 seconds if you change it a tiny bit.
Does this question, as posed, admit the possibility that the answer could be “it depends on what the initial random configuration is”? I suspect that’s what it is: there are states that robustly result in the left side having more particles than the right after 20s.
The bet would then be over the integral of all the random initializations (and random perturbations). I.e. does a random initializations in-expectation leave enough information intact for 20 seconds if you change it a tiny bit.