μ μ i = ( ∂ ∂ F / ∂ ∂ N i ) T , V , where F is not proportional to N because μ μ i depends on pressure. μ μ i = ( ∂ ∂ G / ∂ ∂ N i ) T , P , where G is proportional to N (as long as the molar ratio composition of the system remains the same) because μ μ i depends only on temperature and pressure and composition. μ μ i / τ τ = − − 1 / k B ( ∂ ∂ S / ∂ ∂ N i ) U , V