Hello,

As we know that, an egg conatins a lot of protein. And also, we know that a protein has four kind of structures. In an egg, the white part that is present, is called albumen. When an egg is boiled, the protein helical strucure gets denatured, means it gets broken up. When the coiled structure gets broken, there is a lot of space available. And one property of entropy is that, it increase with open area. Hence entropy increases with heating.

Hope it helps.