When deriving the energy fluctuations in the canonical ensemble, a step is made to approximate Cv≈N, why is this?
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2$\begingroup$ The tilde ~ symbol can be ambiguous unless defined explicitly. The author may be using it to mean "proportional to" or "of the same order of magnitude." In my experience, in official writings it rarely means "approximately equal," because in that case they would use $≈$ $\endgroup$– RC_23Commented May 18, 2022 at 12:44
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$\begingroup$ It can also mean "asymptotic to", but not quite in this case (because that requires the correct prefactors). $\endgroup$– marchCommented May 18, 2022 at 15:53
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1 Answer
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The author indicates that $C_V$ is an extensive quantity, that is, it is proportional to the amount or quantity of material. The latter quantity is indeed $N$, the number of particles in the system.
The constant of proportionality is not mentioned and a clearer way to write the relation could be $C_V = O(N)$.
