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I read that the fluctuation in energy is given by $$ \delta E = E - \langle E\rangle $$

But I don't quite get this. Is this only over one particle? So is E the definite energy of the particle? The last term is of course the average energy so I suppose this is indeed the fluctuation in energy, but how would you generalize this for a system of N particles, and how would you choose E then?

Thanks in advance!

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Fluctuations are generally characterized as a deviation from average. That is, for quantity $Q$ one defines its fluctuation as $$\delta Q = Q - \langle Q\rangle,$$ where $\langle Q\rangle$ is the average. with such definition one obviously has $\langle \delta Q\rangle = $, so one uses either fluctuation squared or the mean absolute deviation to characterize the level of fluctiations $$\sigma_Q^2 = \langle(\delta Q)^2\rangle = \langle Q^2\rangle - \langle Q\rangle^2,\\ MAD = \langle |\delta Q|\rangle.$$

Finally, the fluctuation of energy can be calculated as for a single particle, as well as for the whole system - depending on what $E$ represents in yoru question.

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  • $\begingroup$ Thanks for your answer ! I've one other question :). Suppose I want to calculate the fluctuation squared for N particles. When calculating <Q>^2, do I square the average energy of the whole system, or do I square the average of one particle and multiply it by N? The difference is, I think, that the first will end up with N^2 while the second will end up with N. Thanks! $\endgroup$
    – Caspertijmen1
    Commented Jul 1, 2020 at 11:48
  • $\begingroup$ You use the same quantity for $\langle E^2\rangle$ and $\langle E\rangle^2$ - i.e. both either the total energy or the energy per particle. $\endgroup$
    – Roger V.
    Commented Jul 1, 2020 at 11:54

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