Who is Hermione in Tom Stoppard's Arcadia?
You might like to think about how Hermione, a character who never appears on stage and is only refered to in terms of the affair that Bernard has with her, actually fits into a principal theme of this brilliant play which is that of sexuality and the way that we as humans are often attracted to those that we shouldn't be attracted to. Such attractions represent a force of chaos that threaten to disrupt the ordered nature of the world of this play. Think about the way in which the play refers to many different sexual couplings which all happen offstage. Not only is Hermione's relationship with Bernard one of these, but also Septimus has a rather aptly named "poke in the gazebo" with Mrs Charter. Lord Byron is another character who participates in this sexual coupling.
Such characters, like Hermione, Byron and Lord Croom, are never presented to us onstage and thus are only referred to in the speech of other characters. They therefore remain abstract characters who we as an audience never get to know and therefore are often topics of fun for the characters. The prime example of this is Lord Croom, who thanks to his poor hearing remains completely oblivious to his wife's sexual adventures.
Hermione therefore is rather an unknown quantity in the play that is used, along with other characters, to develop and establish the theme of attraction as a force of chaos in the play.