- #1

phun_physics

- 2

- 1

- 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!

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!