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In a lecture by Purcell he mentions that he notices that there aren't any liquids with viscosities much less than that of water, even though they go up seemingly unbounded. In an endnote (endnote 1 in that copy), he mentioned that Weisskopf found a reason, but I haven't been able to find what that reason actually was.

Note that this is not about the AdS-CFT lower bound.

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If "not much less than water" means "not an order of magnitude lower than water at room temperature" this is probably correct. However there are substances like http://en.wikipedia.org/wiki/Pentane with a viscosity 4 times less than that of water or http://en.wikipedia.org/wiki/Acetone with a viscosity 3 times less than water (at 20 degrees celcius). At lower temperatures (77K) you find liquid nitrogen with an viscosity less than 5 times that of water at room temperature. On the other side at 1K helium becomes a superfluid with effectively zero viscosity http://en.wikipedia.org/wiki/Superfluid_helium-4) In that sense viscosity seems to behave similar to electric resistance, being lower with lower temperature. So without reading Weisskopf I guess it's simply room temperature which provides an lower limit to the viscosity of a fluid.

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