THE CITY OF EQUILIBRIUM: A SCIENTIFIC ALLEGORY AND SELECTED ESSAYS ON PHYSICS (2026)
ISBN: 979-8906064868
I have sometimes wondered whether I use physics to avoid dealing with the world outside it. There is something reassuring about working on a technical problem. You can state your assumptions, work through the mathematics, check a result and understand why something went wrong. Even when you cannot solve the problem, you usually have some idea of what you are trying to solve. Life rarely gives you that much.
I still love physics. But loving something does not mean that every reason for turning to it is a good one. Sometimes I would keep myself busy with research while questions about unfairness, loneliness and the way people treat one another remained unresolved. I could explain why a physical system behaved a certain way. I could not explain why understanding so much about the world seemed to do so little to make it fairer. And I kept looking for explanations, as though finding the right argument would somehow make these things acceptable.
That tension became the starting point for The City of Equilibrium. When I wrote my first book Our Physics So Far, I wanted to understand how the universe worked and share what I was discovering. By the time I began this book, I had spent much more time studying physics seriously. Statistical mechanics and complex systems had become central to my interests. I was fascinated by how interactions between simple parts could produce complex collective behavior, and how apparently random processes could give rise to remarkably consistent patterns. But I was also becoming more conscious of what an explanation leaves out.
In statistical physics, we rarely follow every particle individually. We choose a level of description, keep certain information and ignore the rest. This is an extraordinarily successful way of studying complex systems. Without it, we would often have a mountain of detail and very little understanding. Still, I found myself returning to a question: What happens when we forget that we have made this choice, and when, in our minds, a useful description becomes the whole reality?
Outside physics, we do something similar all the time. We summarize people through their achievements, failures, jobs, grades or behavior in a particular situation. We see the result and miss much of the history that produced it. A person becomes successful or unsuccessful, capable or incapable, normal or difficult. These descriptions may tell us something. But they can also become convenient excuses to stop looking deeper. And this bothered me particularly when thinking about inequality. Science can reveal extraordinary things, but access to its benefits is still shaped by money and power. An MRI machine means very little to someone who cannot afford to visit a doctor. And explaining how a system came to work this way does not settle what we should do about it. I was uneasy about how easily an explanation could turn into a justification, especially when the people most affected disappeared into an average.
The cartoon below takes approximation to a rather unfortunate extreme: A physicist finds the mathematics of his life too difficult and accidentally approximates his life to death. I like the absurdity of it! But it also captures something that kept troubling me while writing the book. We simplify things to make them manageable. At what point have we simplified away the very thing we wanted to understand?
Concept and illustration by me.
These questions became the organizing principle of The City of Equilibrium, which brings together an allegorical novel and five essays on physics. The questions run through both parts, explored through fiction in one and science in the other.
The imagined city in the novel is ruled by Equilibrium, who promises safety through stability. Anything that might disturb the existing order must be managed, including emotions. Grief must remain contained, laughter must not become excessive, and love must not change someone’s behavior in a way the city cannot control. These limits are presented as ways to protect people. That is the central tension: Control becomes difficult to question when everyone has learned to call it peace. The characters in the allegory - Entropy, Temperature, Energy, Mean Field - take their names from physics, but have personalities, attachments and conflicts of their own. I did not want to make approximation itself the villain. Physics depends on it, and so does life. What interests (and disturbs) me is the confidence with which we sometimes decide that the discarded details cannot matter, and what happens when those details actually start to matter in ways we cannot explain away.
There was a more personal question underneath all this too. I have long found nihilism appealing, although I do not mean that nothing is worth doing. I do not expect the universe to provide an inherent purpose for my life. But accepting that intellectually does not make me indifferent to everything that happens around me. I still care about unfairness. I still want to understand things, write, do research and help others pursue their interests. The absence of some ultimate meaning does not remove these concerns. For a while, I kept trying to make that position completely consistent. I wanted an argument that would account for everything I felt and everything I chose to do. Gradually, I became less convinced that such an argument was necessary, or even possible. I think the discomfort comes from expecting reality to make sense in a way it never promised to. The allegory gave me room to explore that discomfort without resolving it cleanly in a way that would feel dishonest. The five physics essays let me examine the scientific ideas more directly and rigorously; I wanted the reader to encounter the actual physics too!
The first essay - Energy, Entropy, and Symmetry - begins with concepts that are familiar enough to sound obvious, until we try to say precisely what they mean. Entropy is often reduced to “disorder,” but that word can conceal more than it explains. The essay looks at how energy and entropy compete, why some processes happen spontaneously, and how symmetry connects with conservation laws.
The next essay - The Method in Nature’s Madness - explores synchronization, collective behavior and phase transitions through the Kuramoto and Ising models. It examines how coupling can bring oscillators with different natural frequencies into synchrony, and how interactions between spins compete with thermal fluctuations to produce magnetic order. What fascinates me is how changing a parameter can lead to a qualitative change in the behavior of the whole system, without any individual part directly causing this change. The essay follows these transitions while examining the assumptions behind the models and the limits of what they describe.
The third essay - The Physics of What We Ignore - is perhaps the essay closest to the central concern of the novel. It asks how statistical mechanics extracts reliable knowledge from incomplete information, and why different microscopic systems can behave similarly at a larger scale. I also wanted to address the question of whether statistical mechanics is merely a convenient tool that physicists use to deal with complex systems, or whether it tells us something fundamental about levels of description.
The next essay - The Past Hypothesis - follows a difficulty that has fascinated me for years: Why does time seem to have a direction? Why do familiar macroscopic processes fail to run backwards? Entropy is central to the discussion, but it brings us to the unusually low-entropy past of the universe, and even more absurd hypotheses like the Boltzmann brain. I wanted the essay to appreciate this foundational question in a rigorous manner, rather than to “solve” the arrow of time.
The final essay - Beyond Quantum Mechanics - returns to a subject that first drew me deeply into physics. Although my current research interests are in statistical physics and complex systems, I still wanted to spend time with the questions that had once occupied so much of my attention. The essay explores quantum foundations, the search for deeper frameworks and the difficulties of bringing quantum theory and gravity together. It also asks what a more fundamental theory could actually explain. Even if we discover the “theory of everything”, there will still be an enormous distance between its equations and an understanding of everything around us.
Writing all this alongside my Master’s coursework, research and other commitments took much more time than I had expected. And frankly, there probably were many good reasons to postpone it. But I also knew that these thoughts would change, and that waiting until I had more time or felt more qualified might mean never writing this particular book at all. So I wrote it while the questions were still bothering me. I have been extremely careful and rigorous with the physics, but I have not tried to make every personal doubt end in a lesson. I would rather a reader disagree with me than come away with the impression that I have found a tidy way to reconcile everything, because I have not. What I am glad about is that I wrote down the tension honestly, moving between wanting to understand the world and wondering what understanding allows us to avoid, between accepting the absence of an ultimate purpose and continuing to care about what happens here. Those questions were taking up a great deal of space in my life. Now they have a book of their own.
- Arpan