In the second expression, the term n ln ⁡ ⁡ n was subtracted and added, using the fact that ln ⁡ ⁡ ℓ ℓ − − ln ⁡ ⁡ n = ln ⁡ ⁡ ( ℓ ℓ / n ) . This was done to highlight exactly how the "entropy" defined here fails to be an extensive property of matter. The first two terms are extensive: if the volume of the system doubles, but gets filled with the same density of particles with the same energy, then each of these terms doubles. But the third term is neither extensive nor intensive and is therefore wrong.