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    • https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/05%3A_Fluctuations/5.01%3A_Characterization_of_fluctuations
      ˜fff=ff=ff0. \[\langl...\boldsymbol{\langle \tilde{f} \rangle \equiv \langle f - \langle f \rangle \rangle = \langle f \rangle - \langle \langle f \rangle \rangle = \langle f \rangle - \langle f \rangle \equiv 0. \label{2}} ˜f2=(ff)2=f22ff+f2=f22f2+f2,
    • https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Thermodynamics_and_Statistical_Mechanics_(Nair)/07%3A_Classical_Statistical_Mechanics/7.06%3A_Fluctuations
      We will now calculate the fluctuations in the values of energy and the number of particles as given by the canonical and grand canonical ensembles. In the end, the fluctuations are small compared to t...We will now calculate the fluctuations in the values of energy and the number of particles as given by the canonical and grand canonical ensembles. In the end, the fluctuations are small compared to the average value as N becomes large.

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