# Derivation of Average Square Energy Fluctuation in a Canonical System

• I
phun_physics
TL;DR Summary
I am currently reading through Chandler's Introduction to Modern Statistical Mechanics and would like insight into this derivation
The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ## \langle( \delta E_v)^2 \rangle## in the attachment.

I am confused on how he went from these steps: ##Q^{-1}(\partial^2 Q / \partial \beta^2)_{N, V} - Q^{-2}(\partial Q / \partial \beta)^{2}_{N,V}## = ##(\partial ^2 lnQ / \partial \beta^2)_{N,V}##

Any help would be extremely appreciated! Thanks!

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