# Where do the terms microcanonical, canonical and grand canonical (ensemble) come from?

Where do the terms microcanonical, canonical and grand canonical (ensemble) come from?

When were they coined and by whom? Is there any reason for the names or are they historical accidents?

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I think it was J. W. Gibbs who first defined them, and probably coined the terms... –  Jellby Jul 17 '12 at 13:19

I'm not completely sure, but I think they are introduced by Gibbs, and that book (available for download) is of historic importance.

The word ensemble really just means "set" in french, you consider the space of canonical coordinates of the detailed mechanics = mircostates and you impose statistics by the fundamental postulate.

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I was trying to read something in that book, but through Google in a reprint... so the right pages were not available. This is what it says in p. xi: "We consider especially ensembles of systems in which the index (or logarithm) of probability of phase is a linear function of the energy. This distribution, on account of its unique importance in the theory of statistical equilibrium, I have ventured to call canonical, and the divisor of the energy, the modulus of distribution." –  Jellby Jul 17 '12 at 13:33
@Jellby: Well good :) –  NikolajK Jul 17 '12 at 13:34
The book definitely looks like the first time canonical and microcanonical ensembles are called by those names. Grand canonical is missing, though. –  Emilio Pisanty Jul 17 '12 at 14:04
Maybe in his "Equilibrium" paper? –  Jellby Jul 17 '12 at 14:36

I do not know where they come from, but in french a canonical form is an expression which appears "naturally". For instance the canonical basis for the linear space spaned by the second degre polynom is made of: {1,X,X^2}

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