tag:blogger.com,1999:blog-13869903.post7049919188712083403..comments2024-03-28T04:15:44.459-05:00Comments on nanoscale views: What is chemical potential?Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-13869903.post-72880596102163953622014-06-04T08:16:48.652-05:002014-06-04T08:16:48.652-05:00Anzel, I think that's basically right. Physic...Anzel, I think that's basically right. Physically, \(\mu\) has units of energy, and in some sense differences in \(\mu\) that are far smaller than the thermal scale \(k_{\mathrm{B}}T\) can't be very important, so you'd expect \(\mu/k_{\mathrm{B}}T\) to be the physically relevant parameter. In terms of formalism, when going from canonical ensemble (system and reservoir exchanging \(E\)) to grand canonical ensemble (system and reservoir exchanging \(E\) and \(N\)), the requirement that \(S\) be a maximum for equilibrium implies both \(\partial S/\partial E\) and \(\partial S/\partial N\) be equal between the system and reservoir. The former is \(\beta \equiv 1/k_{\mathrm{B}}T\), and the latter is \(\alpha \equiv \mu/k_{\mathrm{B}}T\).Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-6142821040725787132014-06-04T04:22:46.182-05:002014-06-04T04:22:46.182-05:00So I can sort of understand the tendency for \mu t...So I can sort of understand the tendency for \mu to be related to energy (if you have a field, it will push particles one way, which would be balanced by the tendency to diffuse). I assume this would be why the \mu/T is the important parameter in looking at flow? The greater the temperature, the greater the tendency to diffuse, so the more chemical potential you need to keep things separate? Anzelhttps://www.blogger.com/profile/11518178405267774499noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-7657810800812872932014-06-03T07:52:45.013-05:002014-06-03T07:52:45.013-05:00Hi Micah - Thanks for the kind words. I've ne...Hi Micah - Thanks for the kind words. I've never been able to bring myself to do twitter, mostly because I'm too verbose for 140 characters. Maybe I should re-evaluate, though.Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-12633089903452303862014-06-02T20:57:58.458-05:002014-06-02T20:57:58.458-05:00Hi Doug, this is Micah Green (former postdoc in Ma...Hi Doug, this is Micah Green (former postdoc in Matteo's group). Are you on twitter? I think your blog would have a farther reach from there. I enjoyed this one on chemical potential.MJGhttps://www.blogger.com/profile/15186044201118240601noreply@blogger.com