Arcadia explores the nature of evidence and truth in the context of modern ideas about history, mathematics and physics. It shows how clues left by the past are interpreted in the present, by both laypeople and scholars. Stoppard has said that his initial inspiration came from reading James Gleick's 1987 bestseller, Chaos: Making a New Science, "which is about this new kind of mathematics. That sounds fairly daunting if one's talking about a play. I thought, here is a marvellous metaphor." Besides chaos, the play attends to a wide array of subjects, including thermodynamics, computer algorithms, fractals, population dynamics, determinism (especially in the context of love and death), classics, landscape design, Romanticism vs. Classicism, English literature (particularly poetry), Byron, 18th century periodicals, modern academia, and even South Pacific botany. These are all concrete topics of conversation; their more abstract resonances rise into epistemology, nihilism, and the origins of lust and madness.
Arcadia's themes are presented in a series of dichotomies. Most prominent is chaos versus order. The play's characters and action embody this, moving from a settled social order, in which relationships arise, toward the final scene, where the social order – and even the separation of the two eras – dissolve in the party's chaos, relationships collapse, and the characters die or disperse. Yet within that chaos, order can still be found. As Valentine declares: "In an ocean of ashes, islands of order. Patterns making themselves out of nothing." Although the play's world grows increasingly chaotic – with overlapping time periods, increasingly complex ideas, and ever greater variations in social norms and assumptions — connections and order can still be discerned. The characters attempt to find and articulate the order they perceive in their world, even as it is continually overturned.
The center-stage table that collects props from both time periods throughout the play is a vivid metaphor of the chaos/order dichotomy. As Paul Edwards, professor of English and History of Art at Bath Spa University, explains: "At the end of the play, the table has accumulated a variety of objects that, if one saw them without having seen the play, would seem completely random and disordered. Entropy is high. But if one has seen the play, one has full information about the objects and the hidden 'order' of their arrangement, brought about by the performance itself. Entropy is low; this can be proved by reflecting that tomorrow night's performance of the play will finish with the table in a virtually identical 'disorder' — which therefore cannot really be disorder at all."
A closely related theme in Arcadia is the opposition of Classicism and Romanticism. This appears most clearly in the running argument between Noakes and Lady Croom about proposed changes to the garden. They all involve moving from the tidy order of Classic style to the rugged naturalism and Gothic mystery of the Romantic. A parallel dichotomy is expressed by Septimus and Thomasina: He instructs her in the Newtonian vision of the universe, while she keeps posing questions and proposing theories that undercut it. Hannah's search for the hermit of Sidley Park also touches on this theme. "The whole Romantic sham!" she passionately exclaims to Bernard. "It's what happened to the Enlightenment, isn't it? A century of intellectual rigour turned in on itself. A mind in chaos suspected of genius ... The decline from thinking to feeling."
Another major theme is the irreversibility of time. Thomasina examines this scientifically, remarking that while Newtonian equations work both backwards and forwards, things in reality – like her rice pudding – cannot be "unstirred." Heat, too, she notes, flows in only one direction (the second law of thermodynamics). This is embodied by the characters, who burn bridges in relationships, burn candles, and burn letters – and in the end, Thomasina herself (like a short-lived candle) burns to death. The finality of things is always present.
Thomasina's insights into thermodynamics and heat transfer, and the idea that the universe is cooling, echo the poem Darkness by her "real life" contemporary, Lord Byron. Written in 1816 — the "Year Without a Summer", caused by atmospheric ash from the volcano Mount Tambora erupting in the Dutch East Indies — "Darkness" depicts a world grown dark and cold because the sun has been extinguished.
The play's end brings all these dichotomous themes together, showing that while things may appear to contradict — Romanticism and Classicism, intuition and logic, thought and feeling — they can exist, paradoxically, in the same time and space. Order is found amid the chaos.