Statistical and Dynamical Physics of the Brain (APS Part 3)

March 17, 2026

Article Preface:

The typical notes here:

Lots of names have been changed for privacy.
The acronym APS stands for the American Physical Society. At the time of this writing, I was attending the annual APS conference in . This article is the third in a series: the first entry is Traveling to Denver, Colorado (APS Part 1); the second is I Got Into a Fight at APS: Science Communication (APS Part 2).

The Statistical and Dynamical Physics of the Brain

Today was the big day. It was time for the big switcheroo of fields: from nuclear physics to biophysics, and hopefully finding room to use the methods of statistical physics. The session that I was on the lookout for today was called Statistical and Dynamical Physics of the Brain. There could not have been a more important session for me and Perry. He was planning to graduate at the end of the fall 2025 semester, and was still deciding if he was going to apply to teaching and research positions or only research positions. He had been carried along for the ride through a river of questionable research trajectories by an advisor who seemed to believe that Dr. Fauci was behind the spread of SARS-CoV-2. The prospect of continuing in research was starting to look glum for him. But he found fascination in neural computation and brain-on-a-chip research; if this session contained appealing prospects, he’d fold postdoctoral positions into the “ordinary job” search in the summer. I, of course, had absolutely no choice: After all of my reading and studying of neuroscience and psychology while actually doing physics in the daytime, this had to become my new field of research.

Felix was also attending this session. Felix and I were similarly obsessed with ideas from physics finding application in neuroscience. The brain is just a fascinating system in the first place. It is not only interesting to find physics succeeding in characterizing neural dynamics, but I also find it philosophically riveting: Remember, a major outstanding problem is the seemingly impenetrable-but-incorporeal thresholds so neatly partitioning the physical sciences, (partly) contributing to the collapse of reductionism. However, if major strides are made in providing an explanatory apparatus to biological systems, then perhaps reductionism is back in full swing.

The session was scheduled to run from 12–3 p.m., which was a nightmare. The session is three hours long?! That’s longer than any class I’ve had! It didn’t matter: I was going to sit through all of them, make a million notes, and ask everybody if they had postdoctoral positions—or any other research opportunities in quantitative neuroscience, neurophysics, or any other type of research that even remotely borders this area. The truth is I could not stomach another day in theoretical hadronic physics. Goodbye forever, symbolic regression!

Lucky for me and Felix, the first talk of the session struck a chord immediately! I couldn’t believe what was happening: A graduate student from Boston University was presenting on the statistical mechanics of reinforcement learning. By analogizing reinforcement learning algorithms to the dopaminergic circuitry of the human brain, he was able to “turn the crank” of statistical mechanics. (I was actually somewhat jealous that this was his actual Ph.D. project. He got to work on this for his actual Ph.D. instead of having it be “dark work” like me? I often blame myself for not doing a thorough enough investigation into the research programs that I ended up applying to. But how could I account for the unknown-unknowns? I applied under the umbrella field “high energy experiment,” with an aspiration that I would learn the techniques required to transition into its corresponding theoretical program. I did not know that I would start finding fascination with neuroscience to the extent that I did. When I argue it from this perspective, I can pump the brakes on my agitation a little bit. But I admittedly do suffer these “elementary agitations” from time to time.)

This methodology was exactly the approach that Felix and I had been appealing to when we did our work on the statistical mechanics of the Lotka-Volterra and the SIS model. My blood was a torrent in my veins. This, right here, I thought. This is it.

The session was fascinating to me. Anything about applying physics to the brain was interesting to me, even if I didn’t find it particularly methodologically sound. First of all, this field of “neurophysics” is relatively new. Secondly, I was evaluating the extent to which the modeling practice incorporated extant neurobiologically-grounded findings; if someone presents an “autonomous neural field theory” connecting the hippocampus and the neocortex, I am going to ask that person if their model allows for the formation of new memories. Lastly, if there’s one thing that’s good about APS, it is that you definitely get a feeling for what kind of research is taking place; it’s relatively holistic, in that sense. Sure, there is some research that may have absolutely no solid basis. But there is also research with an excellent foundation. There are some talks that are incomprehensible. And there are some talks that are wonderfully comprehensible. When all is said and done, though, independent of the quality of the presentation, at least you know what kind of research is out there.

I periodically glanced over at Perry. Like me, he had adopted the habit of taking copious notes on an 8.5-by-11-inch sheet of white paper on top of a semi-solid surface. These days, I had been trying to forego that practice in favor of the active recall approach. But I decided not to appeal to that practice this time around. Since I needed to have a list of specific details to ask some of these speakers about (and because the session was three damn hours long), I resigned myself to actually making somewhat detailed notes. And the talks just kept going. Nobody was pumping the brakes: ten-minute talk after ten-minute talk.

Over time, I saw Perry’s notetaking slow down. Then, he stopped. Then, when he heard that the next talk would be about organoids, he quickly picked up his pencil and wrote down the name of the talk. But even during that talk, his inertia was quenched quickly. This wasn’t working, I thought. This is catastrophic. I wondered if I was witnessing in real time the loss of an excellent physicist to the field that so needed him. I started thinking: Was academic research really as lost as I feared it was? Though I myself could not pinpoint all the technical inaccuracies in these talks, I couldn’t easily conclude that the field was hopeless. But was there something I wasn’t seeing here? As we know, if anyone can assess the quality of the research paradigm, it would be Perry.

Suddenly, Perry nudged me. “Vecta’s talk is now,” he said. Oh! I was so absorbed in our session—not only in the sense of attention, but also in the sense that Perry and I were seated in the exact middle of the audience—that I had spaced out and completely forgot about Vecta’s talk sandwiched (speaking of) in the middle of this session.

I checked the time—already about halfway over, if they were following the schedule at all. Perry shuffled to the exit of the room, and I followed, but I already had major reservations. We made it to the top of the staircase before I conceded to Perry, “Hey, there’s no way we can make Vecta’s talk at this rate; it’s just too far to walk and it’s already too late.” But Perry continued on the path forward, in total futility, at the hopeful (hopeless) prospect that he may catch the last minute of the talk. If you had walked at least one time through the convention center, paying even a smidgen of attention to its (characteristic length) scale, you ought to have some suspicion that there is no way to traverse from its top floor to its bottom floor and out the front door in less than 5 minutes, let alone arrive at the Hyatt Regency’s third floor in time to see Vecta’s talk. One can argue this fact with dimensional analysis alone.

I felt bad that I would miss Vecta’s talk, and that I’d decided not even to try to make it on time. But I know my calculation was correct: Even if I had started right then and there, I would have no doubt missed Vecta’s talk. But the more I ruminate upon it, the more I realize that I might have made a wrong decision: After all, it was feasible that his session was running off schedule. I wouldn’t have known where his session was had I not ventured on over to the Hyatt Regency.

Surprisingly, Perry returned to the session before it ended! Yes… the session was that long. But only a few talks remained at this point.

Finally, the session ended. While everybody rocketed up out of their seat, getting the blood back into their legs, Perry remained seated. I was in that group that jettisoned from the black, plastic chair and started elongating my quadriceps, seeing if they remembered their elasticity that I had spent years cultivating when I was a serious dancer. They did, though I could have used some additional synovial grease. But Perry was still seated. He took off his glasses and rubbed his eyes. I know that look, I thought.

Before people started evacuating the hall, I had to spy on and take note of all the “significant figures” that I needed to speak to about the contents of their presentation. One of them was already pretty close to the aisle here. He would be the first one I approach. Then, I had to talk to the session chair. To my dismay, I discovered that I did not actually remember what the first presenter even looked like. A total shame! How could I have so fallen in love with the research he presented on and not remember to encode what he even looked like?!

“Hey, do you have a quick second to talk about your work?” I started with the spiral wave theorist. He had also mentioned a postdoctoral position available. At the University of Copenhagen, too! What a dream! But work was exotic. And challenging. And complicated. He solved the complex Ginzburg–Landau equation on the neocortex as his background geometry to model the spatiotemporal evolution of so-called “brain spiral waves.” But… they’re brain waves… Why would they be complex-valued? My apprehensions aside, his presentation earlier proceeded in layers of increasing conceptual complexity. That, I appreciated! He started by motivating why solving wave equations on curved surfaces was theoretically interesting, using a cone (with the geometrical singularity at the tip) as an example. It was only after this series of increasingly complex examples that he finally unsheathed the numerical analysis of brain spiral waves evolving on the complicated neocortex, featuring the biologically-grounded geometrical intricacies of our sulci.

There were a few talks on this insanely exotic type of research that used something called “neural field theory.” Sheesh. This is definitely where my skepticism arose. One of my favorite jargon words that I like to whisper to my friends during seminar talks and colloquia is “neurodiffeomorphic,” because it is sufficiently stupid but combines some of the hot topics in physics: differential geometry and neuroscience. It is exceedingly easy to imagine that, because of the relationship of artificial neural networks and neurobiology, that a physicist can come along and present a “neurodiffeomorphic approach” to unifying neuroscience and geometry. And wouldn’t it be beautiful, too?

And, truly, some of these talks reeked of that kind of presentation. However, there isn’t much you can really argue with when it comes to the numerics. And if someone claims to have numerically simulated the dynamical evolution of a scalar (classical) field theory on a fancy, curved manifold, alright then; no $3 + 1$ decomposition needed; no lapse and no shift; no high-dimensional manifold stuff. All of that is to say that I had never heard of “neural field theory” before, but it nevertheless appeared as though it were a full-force research program. Sigh… Another category of research to study.

Our conversation concluded. I can’t entirely remember how it proceeded, to be frank. But he ended with “Shoot me an email!” regarding the open postdoctoral position. Nice! I thought. This could be an opportunity. I don’t know what I can really contribute to brain spiral wave theory, but I needed to give it a shot.

Time to find the session chair!

To be continued…

Notes/References:

“…contributing to the collapse of reductionism.” What exactly does that mean? Well, it helps to know what “reductionism” refers to broadly: It is the idea that everything fancy and complex, made of several different complicated interacting pieces can be reduced all the way down to the most fundamental constituent of matter, which are the subatomic particles. So, we must regard physics as the “most fundamental” science, because chemistry is just applied quantum mechanics, cellular biology is just applied chemistry, and so on. (See XKCD 435.) A good article that discusses this theme is The Truth Physics Can No Longer Ignore. In that article, we also get a brief explanation of what reductionism is:

The central hubris of physics has long been the idea that it is the most “fundamental” of all sciences. Physics students learn about the basic stuff of reality—space and time, energy and matter—and are told that all other scientific disciplines must reduce back down to the fundamental particles and laws that physics has generated.

“…elementary agitations…” This is a physics joke. The real phrase is “elementary excitations,” which are the basic excitations of a physical system above its ground state. I don’t know if I can easily explain much more beyond this, at least right now.
The Lotka-Volterra model is a dynamical system modeling the interaction of two populations: a predator population and a prey population. It is a mathematical model that has been studied for more than 100 years now since it was first introduced. It is super, super famous. To get a decent mathematical appreciation of it, I think the Wikipedia article Lotka-Volterra equations on the subject does a decent job.
The SIS model is the “Susceptible-Infected-Susceptible model” of epidemiology. It is also quite famous, but the “Susceptible-Infected-Recovered model” is even more famous. Again, it is a mathematical model, and it describes the number of individuals who are susceptible to a certain disease and those who already are infected with the disease. The “chronology” of the words describes the “path” of one’s pathology: First, they are susceptible to the pathogen, then they are infected with it, and then they either recover (the SIR model) or they go back to the susceptible state (the SIS model).
“…complex Ginzburg–Landau equation…” Uh, are you looking at me? Ask Wikipedia: Ginzburg–Landau equation.
“…neural field theory…” Again, don’t ask me. All I can say is that, sure, one can imagine modeling the electrochemical potential on the surface of the human cortex using a scalar field $ϕ (\vec{x}, t)$ and call this a “neural field theory.”
“…no $3 + 1$ decomposition needed; no lapse and no shift…” In order to simulate aspects of General Relativity, the theory of spacetime and its matter content, typically researchers use a “ $3 + 1$ decomposition.” It is extremely complicated, and I suffered tremendously during that unit in the Advanced General Relativity class that I audited back in 2023. (Great class, but pretty difficult!) The “ $3$ ” stands for the number of spatial dimensions, and the “ $1$ ” stands for the time dimension. Spacetime is one object—that’s why it’s spelled the way it’s spelled—but it is numerically difficult to work with. So, they “freeze” a particular configuration of space at a given time. Then, they do this again at another instance of time. And again. Through this method of taking “snapshots,” they can piece together the evolution of spacetime without simulating the entire darn thing all at once. The so-called “lapse” and “shift” are fancy vectors that tell us how a surface frozen at one instance of time is oriented with respect to another surface frozen at a different instance of time. By the way, it is a good idea to learn the terminology of “ $X + 1$ dimensions.” For example, in theoretical condensed matter physics, researchers will solve quantum field theories in $2 + 1$ dimensions, which refers to the formulation of the field theory on a two-dimensional space plus one dimension of time. There are fun toy models (field theories) formulated in $1 + 1$ spacetime geometry, the famous example being $1 + 1$ -dimension Quantum Electrodynamics (QED), called the Schwinger model. (Why is the Schwinger model cool? It exhibits the phenomenon known as confinement, an absolutely critical and super interesting feature of an insanely more advanced and complicated theory called Quantum Chromodynamics (QCD) in $3 + 1$ spacetime dimensions.)

Updates:

2026-09-17: Touched up a bit of a strange sentence.