Entropy, time, and the arrow of adolescence

In the months since graduating college, nostalgia has become a major ruling force in my life. And so I have turned to the campus novel. Of the many I’ve consumed, Elif Batuman’s The Idiot and Either/Or have especially lingered in my mind. Batuman’s exploration of this strange, mixed-up period of adolescence rang painfully true to me, especially her depiction of how the formerly distinct aspects of one’s life—school, home, social time, and personal time—become increasingly jumbled in college.

In one scene in Either/Or, the protagonist, Selin, is making tea. She considers how, when one pours milk into the tea, the substances will naturally mix together, so that they are no longer two discrete entities. She has learned in her physics class that, while it would be extraordinarily unlikely for the two to separate, this is not technically impossible. This leads her to reflect on the disorder of her present moment, particularly surrounding a turbulent friendship that has unraveled seemingly beyond repair. She wonders if their relationship, and perhaps her life, can ever resemble its rose-tinted past, if this too rubs up against the borders of possibility.

On the personal, philosophical, and scientific levels, this is a largely unanswered question. Can what has become disordered over time reorder itself? Is there an inherent link between things getting mixed up and the forward march of time?

Physicists would approach this question through the lens of a quantity known as entropy. Entropy is typically defined as the degree of disorder in a system, though some take issue with the misleading connotations of this simplistic definition.

In reality, entropy can be defined in many ways. Perhaps it is best known for its role in the second law of thermodynamics, which argues that all things naturally move toward a state of equilibrium. Heat dissipates; pressure evens out; milk and tea swirl together until they lose their distinct identities. In this thermodynamic definition of entropy, the entropy of a system increases as energy becomes less “usable.” After heat dissipates over a temperature difference, there is no longer as much potential for the system to change; in other words, less potential energy is available to do work on the system.

Is there an inherent link between entropy and the momentum of time? Even further, is entropy perhaps a driving force in time?

Another way of understanding why entropy increases is through statistics. Let’s say we have two types of particles, half of which are blue and half red. They are separated by color, prevented from mixing by a wall between them, which then mysteriously disappears. Once they are free to wander, there are many more possible configurations of the system where the different particles get mixed up than situations in which the particles remain bunched together by color. And so statistics dictates that the distribution of red and blue particles will become more jumbled over time. The system becomes more and more disordered, and entropy increases. Such is the natural drive of the universe.

And so we get to the crux of the matter: is there an inherent link between entropy and the momentum of time? Even further, is entropy perhaps a driving force in time?

These questions are particularly exciting for physicists, given that fundamental physical laws don’t account for the forward “arrow” of time; time is treated as a quantity just as position or momentum is. However, you can always return to your initial position or momentum. You can’t return to your initial time.

Historically, physicists have speculated that entropy might play a role in the irreversibility of time. Since Sir Eddington’s 1927 assertion that entropy is what propels the arrow of time, this assumed relationship has more or less stuck around. It’s what undergirds the theory of the eventual heat death of the universe, when the universe has reached a complete equilibrium where all things are mixed and there is no more usable energy.

However, many have also challenged this idea. In a 2020 paper, Arieh Ben-Naim, a chemistry professor at the Hebrew University of Jerusalem, delves into the different ways entropy has been defined (including its thermodynamic and statistical definitions). 

Given that none of the major equations used to define entropy have an explicit time dependence, Ben-Naim argues, one cannot prove for certain that entropy and time are linked. In fact, contrary to the AP Chemistry official line, Ben-Naim does not even take for granted that the overall entropy of the universe is always increasing. 

In a 1975 article for Scientific American, David Layzer, who was a Harvard professor of astrophysics, also pushes back against the idea of an innate connection by exploring two different arrows of time: the “historical” arrow and the “thermodynamic” arrow. 

The historical arrow of time describes how systems become more complex over time, such as how life formed on Earth. However, to Layzer this increase in complexity suggests a historical increase in order, not disorder. 

The thermodynamic arrow of time, which Layzer essentially takes to mean entropy, contradicts the historical arrow of time, as it implies a natural increase in disorder. In order to resolve this disjunction, Layzer proposes that we replace the idea of the universe melting into a homogeneous puddle of nothing with a vision of the universe as “unfolding in time but not unraveling; on the contrary, it is becoming constantly more complex and richer in information.”

On the macroscopic level of the universe’s life and the microscopic level of my life, I find the latter idea far more appealing. In Batuman’s books, Selin’s process of growing up may seem disjointed, but it’s perhaps even more constructive than it is destructive. As relationships and worldviews crumble, new, often better kinds of connections and ways of living are also revealed.