In Arcadia, Stoppard presents his audience with several highly complex but fundamental mathematical and scientific concepts. He also uses these theories and ideas to illuminate relationships among his characters, adding to their poignancy.
One of the play's main thematic concepts is chaos theory. Paul Edwards, in his essay "Science in Hapgood and Arcadia", notes that "chaos mathematics is about the recovery of information from apparently chaotic and random systems where entropy is high. [...] It is 'asymmetric' (unlike the equations of classical physics), yet it finds regularities that prove to be the regularities of nature itself. Strikingly, this mathematics can generate patterns of amazing complexity, but it also has the power to generate seemingly natural or organic shapes that defeat Newtonian geometry. The promise, then, (however questionable it is in reality) is that information, and by extension, nature itself, can overcome the tendency to increase in entropy".:181
John Fleming, in his book Stoppard's Theatre: Finding Order amid Chaos, makes a similar observation. "Deterministic chaos", he writes, "deals with systems of unpredictable determinism. ... [T]he uncertainty does not result in pure randomness, but rather in complex patterns. Traditionally, scientists expected dynamic systems to settle into stable, predictable behavior." But as systems respond to variations in input, they become more random or chaotic. "Surprisingly, within these random states, windows of order reappear. [...] There is order in chaos — an unpredictable order, but a determined order nonetheless, and not merely random behavior."
Closely related scientific and mathematical concepts in Arcadia are the second law of thermodynamics and entropy. Fleming describes these two principles. "Entropy is the measure of the randomness or disorder of a system. The law of increase of entropy states that as a whole, the universe is evolving from order to disorder. This relates to the second law of thermodynamics, which states that heat spontaneously flows in only one direction, from hotter to colder. Since these equations, unlike Newton's laws of motion, do not go backward and forward, there is an 'arrow of time' that points toward the eventual 'heat death' of the universe."
In Arcadia, Stoppard uses all these concepts to reveal that "there is an underlying order to seemingly random events." The characters discuss these topics, while their interactions reflect them.
Some ideas in the play recall Goethe's novella Elective Affinities: Stoppard's characters "Thomasina" and "Septimus" have parallels in Goethe's "Ottilie" and "Eduard", and the historical section of Stoppard's play is set in 1809, the year of Goethe's novella.