We will study the way in which the entanglement entropy of a holographic quantum system becomes the thermodynamic entropy, at finite temperature, as we vary the size of the entangling region. For this purpose, we will concentrate on the holographic entanglement entropy using the Ryu - Takyanagi prescription. We will study the holographic entanglement per unit volume, to understand how the Infrared degrees of freedom can affect the way in which the entanglement entropy becomes extensive. In particular, we will show that the holographic entanglement density will become over - extensive and develop a peak, for intermediate scales.