New book: Introduction to Ergodicity Economics

An Introduction to Ergodicity Economics is a new textbook that draws on physics to re-examine traditional economic theory. It begins with flipping a coin. And a hypothetical gambit. Imagine you were offered the following: Every time the coin lands on heads, your wealth increases by 50%. And every time tails comes up, your wealth drops by 40%.

Should you accept?

It depends on how you look at the predicted outcomes of this random system, says SFI Professor Ole Peters, a physicist at the London Mathematical Laboratory, who co-wrote the textbook with Alexander Adamou, a former LML colleague. The textbook was published in June 2025.

One way to characterize how your wealth will change in the coin-flip scenario, says Peters, is to follow an individual’s progress over time and average the value. This is the time average. A different way is to calculate the expected value, which means calculating the average wealth of many systems at one time (say, 100 flips into the future).

These may not yield the same results: When randomness drives outcomes, expected value can rise even as the time average for an individual plummets. Peters likens this to a relatable, real-world phenomenon. “A government may say, Isn’t the economy doing great? And the individual worker says, I don’t really see that in my paycheck,” he says.

The tension between the time average and expected value forms the basis for a theory of ergodicity economics, which Peters has been developing for nearly 20 years. The term ergodicity describes what happens when the time average and expected value align, which means one is replaceable with the other, and the behavior of an individual system can be modeled by the average behavior of a collective. Austrian physicist Ludwig Boltzmann first introduced this concept in the 1870s, in the context of thermodynamics, to describe a physical system.

But ergodicity is a special case, Peters argues, and there’s no reason to assume that the two will uniformly agree. Many systems, especially in economics, may be non-ergodic — like Peters’ coin flip-for-wealth-or-poverty example. Broadly, says Peters, there is a longstanding tension in conomics between a dominant framework around expected-utility theory, with roots in the 18th century, and 20th-century challenges to this framework that question human rationality (or even the use of formal models) in describing economic processes. Ergodicity economics offers a third way.

As a physicist, Peters had previously studied statistical mechanics, an area focused on how lots of tiny particles, moving randomly, give rise to predictable, observable behaviors. But starting around 2006, he began to find ways to use those ideas to re-examine long-held ideas in economics, particularly around how people make decisions.

He found that economic models often assume ergodicity as a starting point. For An Introduction to Ergodicity Economics, the first textbook in the field, Peters and Amadou present a formal challenge to that assumption, using mathematical rigor and careful examples to show how non-ergodicity can arise naturally — and how it can be addressed in models. 

“We have this radically different starting point. We break this formal assumption and start new, but just as formally,” he says. “My hope is that the book will help people see this other perspective because without it, I fear that economics is not succeeding in solving our most pressing problems.”

More

Ole Peters introduces the new textbook on his YouTube channel Ergodicty TV.

Reviews

• Andreas Loeffler reviews the textbook in "Notes on Ergodicity Economics" (August 16, 2025). 
• Lars P. Syll reviews the textbook on the blog post "At last: the first-ever textbook on ergodicity economics" (September 22, 2025)