Happy New Year! It is time for the traditional post about our last year's yield. And its still quite good. Though this year, I received some help from my colleague Vygintas Gontis who wrote four posts on macroeconomics and prepared one interactive app.

Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk (as of the end of 2025). The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts containing an interactive app.

We have started the year with various modifications of the Colonel Blotto game. This series of posts culminated in Colonel Blotto moving to an adjacent field of sports. Next we have discussed periodic polling effects and information delay in the noisy voter model [1]. While in the autumn, we have had couple of posts on various assorted topics.

What's next? Still, I am bit overwhelmed and have no concrete plans, but occasionally I'll post something interesting.

References

• A. Kononovicius, R. Astrauskas, M. Radavičius, F. Ivanauskas. Delayed interactions in the noisy voter model through the periodic polling mechanism. Physica A 652: 130062 (2024). doi: 10.1016/j.physa.2024.130062. arXiv:2403.10277 [physics.soc-ph].

In this Numberphile video prof. Marcus du Sautoy talks about mathematics behind the board game he likes to play with his kids. What a better way to spend winter holidays, than playing board games? Watch the video not only to gain competitive edge, but also to see how serious mathematics (and physics) can be applied to a fun casual activity.

Over the last few posts I have been writing about variety of research conducted by a group based in University of Catania. I have covered some of their models illustrating various often counter-intuitive effects of randomness within social systems. This time let us talk about how a certain degree of randomness could benefit our political life [1].

Global economic media frequently report that U.S. productivity has been growing much faster than in Europe and other developed Western economies for many years. As an example, consider the recent publication in the Financial Times (FT). This is not journalistic exaggeration—such conclusions follow directly from the still widely used methodology of calculating real GDP and productivity, and from international comparisons based on that methodology.

The FT article clearly illustrates that Europe's economic lag behind the United States is treated as an objective reality at the highest levels of politics, and that policymakers have been searching for ways to "close this gap" for many years. We present these remarks because doubts about the magnitude of the United States’ economic advantage naturally arise from the study of international macroeconomics and economic growth theory.

Our most recent work [1] concerning the first passage time problem in the noisy voter model has been published in Chaos, Solitons and Fractals!

The mean first passage time is a prominent tool that quantifies fundamental switching behavior in systems ranging from natural to social sciences. In our earlier works the first-passage framework has found applications as a test for long-range memory [2]. While, the noisy voter model is a prominent model used to understand human opinion dynamics.

References

• R. Kazakevicius, A. Kononovicius. Mean first passage time of the symmetric noisy voter model with arbitrary initial and boundary conditions. Chaos, Solitons and Fractals 203: 117649 (2026). doi: 10.1016/j.chaos.2025.117649. arXiv:2512.02519 [cond-mat.stat-mech].
• R. Kazakevicius, A. Kononovicius, B. Kaulakys, V. Gontis. Understanding the nature of the long-range memory phenomenon in socio-economic systems. Entropy 23: 1125 (2021). doi: 10.3390/e23091125. arXiv:2108.02506 [physics.soc-ph].