lets start with Schrodingers Cat
General: both of these eggs were found in the mathematics section of the keep's library. nobody knows how they got there.
Schrodinger's Cat
Egg:
description: this egg is striped, with tabby stripes slanted from left to right. or is it right to left? everytime you look at it there's a fifty-fifty chance it'll have changed directions
Hatchling:
description: it looks like a regular kitten - from the hips back. it has two fronts, however. the right one is alive, and the left one is dead. or is the left one alive and the right one dead? each time you refresh the page, you'll have a fifty-fifty chance of it switching alive and dead ends. the dead end would look freshly dead - no matter which end it was or how long its been dead.
The egg has hatched. you stare, slightly dumbfounded at the creature that has emerged. it looks like a siamese twinned cat - but one half is dead. you gather the kitten up and set it on your shoulder, where it somehow manages to stay on, even while you are doing other things. you creep yourself out when you keep glancing at it and the dead and live twins seem to switch. any attempt to remove the kitten from your shoulder will result in the kitten digging its claws in to stay on.
Adult
description: looks like a regular black&grey tabby cat - from the hips back. it has two fronts (that is, two heads, two trunks, two sets of forelegs). The left one is alive and the right one is dead. or is it the other way around? each time you refresh the page, it'll have a fifty-fifty chance of switching dead and alive heads. the dead end would look freshly dead, no matter how long it has been dead or which head it is.
The kitten has grown up and moved off your shoulder. it now moves about the keep as any normal cat would -but you still cant figure out which head is alive and which head is dead.
Maxwell's Demon
Egg
description: it has the shape of an egg, yet abstract physical equations are weaving and scribbling themselves all over it. they move even as you watch. also, when you touch the egg, it feels neither hot nor cold, but the exact temperature of your hand
Hatchling
description: the egg has hatched. or has it? the equations have lifted themselves off the shell, which then broke into pieces, almost as if the equations had been holding it together. nothing came out of the egg, but the equations have arranged themselves into the vague outline of a small black dog.
The egg has......hatched? you stare as the small outline of a puppy comes running over and leaps in your lap. it feels odd to the touch, with some places being as smooth and soft as corn silk, with other places grating like shark skin and still other places pointy as a needle. As you pet it, you notice that, like the egg, it seems to have no temperature of its own, but rather be the exact same temperature as your hand. you also notice that the same thing seems to be happening to the air around it.
Adult
description: the equations have gotten even longer and more abstruse. They have also arranged themselves into the larger shape of......well, you cant really tell. it has four legs, a tail, and a head. it looks vaguely like a large wolfhound. Not that it matters much. it spends most of time laying down, standing only when asked a question.
Your cute little equation-puppy has grown up. now it can control its temperature changing nature, and make the keep as pleasant a temperature as you can ask for. It also has developed enormous magikal power, which it will give to you unstintingly if you have earned its loyalty. it only stands up when you ask it a question - yet it will always be by your side when you call for it.
(i'll include more later. if i think of anything. and no, i probably wont have pictures - i am not le artiste and these you probably couldnt find on teh interwebs)
the actual theories that these creatures come from
Schrodinger's Cat:
Basically, Schrodinger's Cat is a thought experiment made up by a scientist named (you guessed it) Schrodinger. It underlines the flaws in the then-current theories of quantum mechanics. It basically says that you dont know what exactly is going to happen until it actually happens, and that the possibilities both exist simultaneously exist before the action - in this example, two cats would be placed in two separate boxes in two separate rooms. you wouldn't know which cat was alive or which one was dead until you opened the box. before you opened the box, the cat would be both alive and dead. the way i set it up, loading the page would hold the equivalent of opening the box, and each of the siamese twins represents the two different cats in the actual experiment.
Maxwell's Demon:
Maxwell's demon is another thought experiment, this one talking about the laws of thermodynamics (hot&cold stuff). basically, the scientist Maxwell theorized that the eventual equalizing of temperatures of two gasses might be explained by having a sort of gatekeeper (the Demon) directing the molecules of the gasses through a membrane, eventually making sure that both gasses have exactly equal amounts of kinetic energy (heat).
Spoiler
Picture of fullgrown Maxwell's Demon by munin, thank you very much Munin
Like Lupin I would say add a little more to the adults.. thats it though, they are really cool 
*Here (Should) Be Monsters* 