There must be chaotic amplification of quantum events going on. Any macroscopic system at finite temperature will be full of quantum events, like a molecule in an excited state returning to its ground state. The quantum randomness is a constant source of "noise" which normally averages out, but sometimes there will be fluctuations away from a mean, and sometimes they will be amplified into mesoscopic and macroscopic difference. This must be true, but it would be best to have a mathematical demonstration, e.g. that the impact of quantum fluctuations on the transfer of heat through an atmosphere will amplify into macroscopically different weather patterns on a certain timescale.