Well, I'm guessing that your definition of an egg being "cooked" is when it turns from liquid to rubbery, rather than anything to do with killing bacteria that might be present, or any of the other chemical changes involved in cooking:
Basically, what cooking an egg does is denature the proteins that are present. Some of the science is here:
http://www.scienceofcooking.com/eggs/eggs_sous_vide.htm When the egg proteins are denatured, enough energy has been added that the intramolecular bonds which hold the protein into its folded, globular conformation are broken down, and the protein stretches out. That allows it to interact with other, similarly stretched out proteins, forming three-dimensional networks of proteins throughout the egg and making it rubbery.
There are other ways of denaturing proteins besides heat - two of them are described thoroughly in the links I gave you earlier. I have no idea what you are looking for beyond that. Possibly drying? The egg is mostly water which normally keeps the proteins separate - if the water is removed, they can also interact and form networks, but I'm not sure I would consider a dehydrated egg "cooked". There is also mechanical force - beating egg whites causes the same denaturation and extension of intermolecular protein bonds to form a nice stiff foam, but again, I'm not sure I would call it cooking.