Regensburg 2025 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 4: Urban systems, Scaling, and Social Systems

SOE 4.4: Talk

Tuesday, March 18, 2025, 10:30–10:45, H45

Dynamical Power Laws in a Multiplicative Growth Model with Resets — •Alexander Jochim and Stefan Bornholdt — Institute for Theoretical Physics, University of Bremen

The observation that wealth distributions follow power laws -- dating back to Pareto's 1897 work -- has long intrigued physicists, offering a glimpse of universal principles in complex systems. Models based on multiplicative growth with resets are well-known for generating these heavy-tailed distributions, where the power-law exponent depends on the underlying parameters. Yet, such models often treat societal influences as static, ignoring the dynamic feedback between wealth and social behavior.

In this work, we introduce a minimal model where multiplicative growth with resets produces a wealth distribution that evolves dynamically through coupling to social mechanisms. This adaptive feedback leads to time-dependent power-law exponents, reflecting the interplay between wealth inequality and shifting societal behaviors. Our approach captures emergent phenomena in a non-equilibrium toy model for how collective social behaviors influence -- and are influenced by -- the statistical properties of wealth.

By framing wealth distributions as part of a coupled dynamical system, this work connects statistical physics with the study of adaptive social systems, offering fresh perspectives on the evolving patterns of inequality.

Keywords: Society; Wealth; Power Laws; Political Instability; Opinion Dynamics