# Mechanism of Hawking's radiation and entropy of the black hole

During Hawking's radiation, a virtual particle with negative energy and mass (from pair of particle and antiparticle) fall into black hole and its real partner having positive energy escape from vicinity of black hole. And it appears to have been emitted from black hole. Since these pair of particles were present outside the black hole, flow of negative energy particles reduces its mass. As the black hole loses its mass the area of event horizon gets smaller. And so, it must decrease the entropy of the black hole.

So, how the entropy of the black hole always increase? What I am missing here. Please explain.

$$\frac{dA}{dt} \ge 0$$