Consider a system of fixed volume I thermal contact with a reservoir. Show that the mean square fluctuation in the energy of the system is

<(ε – < ε >)²> = τ²(∂U/∂τ)_V                       (89)

Here U is the conventional symbol for <ε>.

not fluctuate in value when the system is in thermal contact with a reservoir Any oilier attitude would be Lncon5itent with our definition of the temperature of a system. The energy or such a System may fluctuate, but the temperature does not. Seine workers do not adhere to a rigorous definition of temperature. Thus Landau and Lifshitz give the result

<(Δr)²> = τ²/Cv

but this should be viewed as just another form of (89) with Δτ set equal to ΔU/Cv. We know that W ΔU = CvΔτ, whence (90) becomes <(ΔU)²) = τ²Cv which is our result (89).

1.0 0.5 0.5 1.0 1.5 Reat capacity, in units of k