Rebecca Carstens, Raj Deshpande, Pau Esteve, Nicoló Fidelibus, Sara Linde Neven, Ramona Ottow, Lokamruth K.R., Paula Rodríguez-Sánchez, Luca Santagata, Javier M. Buldú, Brennan Klein & Maddalena Torricelli
Scientific Reports (2026)

Elite football is believed to have evolved in recent years, yet systematic evidence for the pace and form of that change remains sparse. Drawing on event-level records for 13,018 matches across ten top-tier men’s and women’s leagues in England, Spain, Germany, Italy, and the United States (2020–2025), we quantify match dynamics through two complementary lenses: conventional performance statistics and pitch-passing networks that track ball movement across spatial regions of the field. Between 2020 and 2025, average passing volume, pass accuracy, and the proportion of passes made under pressure all increased, with the largest year-on-year changes occurring in women’s competitions. Network measures reveal that normalized outreach decreased, indicating teams increasingly concentrate ball circulation into shorter-range passing connections rather than wide spatial distribution. These trends are consistent across countries and tiers, yet persistent national differences indicate that stylistic diversity remains. Notably, women’s competitions exhibit stronger rates of change across most metrics, consistent with an accelerating professionalization, while the systematic decline in network outreach across all competitions is consistent with a sport-wide shift toward shorter, more concentrated passing structures.

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Klaus Jaffe

Money serves several roles: a medium of exchange to buy and sell without bartering; a unit of account to price goods consistently; a store of value to save purchasing power over time; a means to defer payment of future obligations like credit or loans. An agent based computer simulation program determine quantitatively the relative importance of these services. The main results showed that money for credit was by far the feature that achieved the largest overall production of wealth in the simulated societies. A conclusion from this study suggests that fomenting the use of internationally tradable currencies such as Bitcoin seems to be most promising pathway for international economic growth in the near future.

Read the full article at: papers.ssrn.com

Qianyang Chen, Mikhail Prokopenko

Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organising system can convert consumed energy into macroscopic order. We study an information-theoretic quantity that directly addresses this challenge by estimating the entropy reduction induced by a small control-parameter perturbation, relative to the generalised work required for the perturbation. This quantity has previously been considered mainly in an equilibrium or near-equilibrium context, and here we extend this framework and apply it to two nonequilibrium self-organising systems: persistent and active Ising models. We observe that the thermodynamic efficiency of nonequilibrium systems maximises at phase transitions, as in equilibrium systems. Furthermore, we compare thermodynamic efficiency and inferential efficiency across control parameters. While these two quantities are equal in equilibrium as a consequence of the fluctuation-dissipation theorem, we report that they diverge out of equilibrium, and the gap reflects how far the system is from equilibrium.

Read the full article at: arxiv.org