The variance in particle number, σ σ N 2 = ⟨ ⟨ N 2 ⟩ ⟩ − − ⟨ ⟨ N ⟩ ⟩ 2 , is: σ σ N 2 = k B T ( d ⟨ ⟨ N ⟩ ⟩ d μ μ ) V , T = exp ⁡ ⁡ ( ( ε ε − − μ μ ) / k B T ) ( exp ⁡ ⁡ ( ( ε ε − − μ μ ) / k B T ) − − 1 ) 2 = ⟨ ⟨ N ⟩ ⟩ ( 1 + ⟨ ⟨ N ⟩ ⟩ ) .