Statistical Mechanics · Problem 3.2

The Grand Canonical Ensemble — R. K. Pathria

Physics — Statistical Mechanics · canonical-ensemble-energy-fluctuations

Problem

Prove that the quantity

g''(x_0)

, see eqn. (3.2.25), is equal to

\langle (E - U)^2 \rangle \exp(2\beta)

. Hence show that eqn. (3.2.28) is physically equivalent to eqn. (3.6.9).