From: Sent: To: Subject: jeffrey E. <[email protected]> Monday, July 6, 2015 10:53 AM Re: thanks, I met with misha gromov. . =if we are talking about the space of probablites and i underst=nd its only a metaphor. but if the information is widely dispe=sed. are their truly independent probabilites.? =AO and music is also probably constrained by an upper volume, =C2 i never thought of it . some limitation on sound waves interacting.=C2 mu guess is there is an upper limit, certainly ver= loud would drown out very soft. etc. great work thanks<=r> On Mon, =ul 6, 2015 at 9:59 AM, Seth Lloyd > wrote: <=lockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-Ieft:lpx=ttccc solid;padding-left:lex"> Dear Jeffrey, =div>My apologies for not responding sooner. I took an email v=cation for a week plus which turned out to be a mistake be=ause I fell irrevocably behind. That was a very f=n conversation with Noam in Cambridge: he is an amazing thinker (if a tad =nflexible at times). Your question about entropy =s an important one. The second law of thermodynamics tells us that<=div> systems go to states of high entropy where events are random and =ncorrelated, so that thermal fluctuations appear to be statistic=lly independent. However, if you look under the hood of t=e second law, you find that what is really going on is that the dynamics</=iv> that leads you to this high entropy state is actually generating h=ge amounts of correlations between the different parts of the sy=tem. In fact, the apparently random and independent fluctuations of the parts reflect large correlations with the other=parts of the system. But these correlations are effective=y smeared out over the whole system: to reveal the fact that they are not truly independent, one would have to make measurements on all the=parts together, and tease out the extensive but subtle correlati=ns between them. For example, even t=ough the apparent high entropy of a gas of molecules reflec