Incarceron by Catherine Fisher

Two fantastic stories weave themselves into one.  Finn tells the tale from inside Incarceron—an experimental prison which was intended to provide a perfect place in which to seal “undesirables.”  Unfortunately for those inside, the experiment has failed and conditions have deteriorated for generations. Finn finds a key to the outside and plots escape.  Claudia (who happens to be the warden’s daughter) tells her story from the outside where civilizations is artificially kept to the conventions of the 17^th-century.  She also plots to escape—from the archaic rules and arranged marriage intended for her.  A beloved tutor, Jared, joins her efforts to uncover the treacherous secrets of her father.  With a key matching Finn’s, she finds a way to communicate with him and help him realize his plans to discover the truth.