Blundell Thermal Physics · Problem 22.1

The chemical potential

Physics — Statistical Mechanics · grand-canonical-ensemble-entropy-maximization

Problem

Maximize the entropy

S = -k_\mathrm{B}\sum_i P_i \ln P_i

, where

P_i

is the probability of the

i

th level being occupied, subject to the constraints that

\sum P_i = 1

\sum P_i E_i = U

, and

\sum P_i N_i = N

to rederive the grand canonical ensemble.