Economics Puzzle Reveals New Physics Insights

Researchers show Boltzmann distribution is the only theory that accurately describes unrelated systems

Feb. 5, 2026 at 11:55pm

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Economists Omer Tamuz and Fedor Sandomirskiy have discovered that the Boltzmann distribution, a law used widely in physics, economics, and other fields to model systems with random and unpredictable behavior, is the only theory that accurately describes unrelated or "uncoupled" systems. Their mathematical proof, published in the journal Mathematische Annalen, shows that the Boltzmann distribution is the only physical theory that is not nonsensical and the only economic model that correctly predicts independent choices in unrelated situations.

Why it matters

This research bridges the gap between economic theory and physics, demonstrating how abstract mathematical thinking can uncover insights that are applicable across disciplines. The finding that the Boltzmann distribution is the only viable theory for modeling unrelated systems has important implications for how scientists and economists approach modeling complex, random phenomena.

The details

To test alternative theories to the Boltzmann distribution, the researchers used "crazy" dice like the Sicherman dice, which have unconventional number combinations but the same probability distribution of sums as regular dice. By showing that the Boltzmann distribution is the only theory that produces the same probability distributions for both regular and crazy dice, they were able to rule out all other potential theories and prove the Boltzmann distribution is the sole accurate model for unrelated systems.

  • The research was published in the journal Mathematische Annalen in 2026.

The players

Omer Tamuz

A professor of economics and mathematics at Caltech who co-authored the research.

Fedor Sandomirskiy

A former Caltech postdoc who is now an assistant professor of economics at Princeton University and co-authored the research.

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What they’re saying

“This is an example of how abstract mathematical thinking can bridge different fields-in this case, linking ideas from economic theory to physics.”

— Omer Tamuz, Professor of Economics and Mathematics, Caltech

“We didn't know what to expect when we started this. We were intrigued by these paradoxical predictions and wondered what it meant for a theory to not have any. In the end, we learned that it means that it has to be Boltzmann's theory. We found a new angle on a concept that has been a textbook staple for over a century.”

— Fedor Sandomirskiy, Assistant Professor of Economics, Princeton University

What’s next

The researchers plan to further explore the implications of their findings and how the Boltzmann distribution can be applied to model unrelated systems in both physics and economics.

The takeaway

This research demonstrates the power of interdisciplinary collaboration and the ability of abstract mathematical thinking to uncover fundamental insights that bridge different fields of study. The finding that the Boltzmann distribution is the only viable theory for modeling unrelated systems has far-reaching implications for how scientists and economists approach complex, random phenomena.