Lipton asks for a physical proof of $P\neq NP$. Can we even ask for a physical proof for understanding $P=BPP$ or $P\neq BPP$? Is there anything in physics that lets us avoid randomness? Statistical mechanics and hence entropy is founded on randomness. Entropy, information and randomness are all related and in this case can physical principles show $P=BPP$ or $P\neq BPP$ let alone the harder $P$ versus $NP$?(Harder is relative here.. the guess here is that $P=BPP$ and $P\neq NP$ and showing classes that are hypothetically closer to be equal may be easier than showing classes that are hypothetically far-off to be separate).
Physical Proof for P versus BPP
cc.complexity theory;complexity classes;it.information theory;randomness;derandomization