Symbolism, Imagery, Allegory
The what and the what now? Okay, let's start by a getting a handle on what these two scientific concepts even are. We're going to get a little science-y; bear with us.
The concept of entropy that is described in the book comes from thermodynamics. In thermodynamics, entropy is a measure of how evenly heat is distributed in a system. The Second Law of Thermodynamics states that entropy will never decrease and that things will tend to disorder (non-convertible energy) and sameness. So entropy is shorthand for both disorder and sameness.
But we need to make sure we understand one basic thing about entropy before moving on to the concept of Maxwell's Demon. Imagine that a "box" of hot fast-moving air molecules is connected to a "box" of cold slow-moving air molecules by a small door and isolated from the rest of the universe. Since the Second Law says that entropy will never decrease, one would expect that the hot and cold molecules would eventually become evenly distributed between the two boxes.
In the late nineteenth century, a Scotch physicist named James Clerk Maxwell came up with a thought experiment to try to disprove the Second Law of Thermodynamics. As above, two boxes of air molecules are brought together, but here the hot and the cold are all randomly distributed. Maxwell postulated that a Demon could sit at the door between the two boxes and open it selectively so that all the hot molecules become concentrated in one box, and all the cold molecules become concentrated in the other.
As Nefastis puts it in the book:
"Since the Demon only sat and sorted, you wouldn't have to put any real work into the system. So you would be violating the Second Law of Thermodynamics, getting something for nothing, causing perpetual motion." (4.17)
In reality, physicists went back and forth arguing whether or not the Demon did or do not "put any real work into the system." The basic conclusion was that the act of sorting would increase the entropy of the system.
But Nefastis goes on:
"Entropy is a figure of speech, then, a metaphor. It connects the world of thermodynamics to the world of information flow. The Machine uses both. The Demon makes the metaphor not only verbally graceful, but also objectively true." (5.20)
This may sound a little like mumbo-jumbo, sort of a word salad. But the key thing to remember is that Nefastis (and Oedipa, to an extent) believe that this ability to properly sift and sort information can keep things from reducing to disorder and sameness.
For Oedipa, Maxwell's Demon becomes a metaphor: a way of imagining her attempt to sift and sort through all of the information that is presented to her in the course of the book—and there is a lot.
Imagine that American history as we know it tends towards sameness, and that everything exists exactly the way we think that it does. The conspiracy of the Tristero would disprove this… much like the thought experiment of Maxwell's Demon claims to disprove the Second Law of Thermodynamics.
But, for the Tristero to be real, Oedipa has to function as the "Demon." Instead of sorting fast and slow-moving air molecules Oedipa is sorting significant and insignificant facts.
Toward the end of the book, Oedipa again begins to think of her dilemma in metaphorical mathematical terms. As she says,
It was now like walking among matrices of a great digital computer, the zeroes and ones twinned above, hanging like mobiles right and left, ahead, thick, maybe endless. (6.148)
She begins to doubt whether all this sifting and sorting is even worth it. It seems endless, with the facts to be examined simply multiplying in number as the book goes on. And Oedipa begins to doubt that all of this will add up to a sense of meaning, to a moment of revelation. She realizes that she herself is necessary for Tristero to exist, that she is its Demon, but if she lets it all go… who cares?
The way that Pynchon plays with the concepts of entropy and Maxwell's Demon turns both of them into crazy metaphors for the way Oedipa relates to the overwhelming amount of information she encounters. Both concepts appear in Pynchon's novel Gravity's Rainbow, and both are general references in a lot of popular fiction, from Isaac Asimov to Ken Kesey.