Eloise was Daniel Faraday's lab rat at Oxford University's Queen's College Physics Department in 1996. Her consciousness was sent forward in time, allowing her to run a maze perfectly, having supposedly been taught the course by Faraday one hour in the future. Later in the day, Eloise died. The cause was unknown, but Faraday hypothesized she had suffered a brain aneurysm. According to his theory, not having any constant, her consciousness couldn't differentiate between the future and the present. ("The Constant")
An Oxford janitorial custodian had the job of incinerating Faraday's dead subject rats so that no one would discover the purposes and results of his experiments. ("Jughead")
The name "Eloise" may come from the movie The Million Dollar Hotel, the movie in which Jeremy Davies (Daniel Faraday) stars. He plays the character of Tom, who is in love with a woman named Eloise.