Multifractal Phase Transitions for the “Transformative Shift” Towards a Shared Value Economy

International projections indicate that extreme climatic events will become more frequent and intense, leading to significant disruptions in water cycle patterns. At the same time, water remains the only irreplaceable natural resource. As a result, human economies must be prepared to confront a range of socio-economic challenges stemming from changes in the water cycle. These issues cannot be resolved through incremental improvements to existing measures. Consequently, there is a growing call for "transformative change" — a comprehensive, system-wide restructuring at various scales, akin to what physicists describe as a non-equilibrium phase transition in a complex, nonlinear system — to tackle the interconnected and persistent challenges.

In recent years, there has been a growing global emphasis on funding research with greater "transformative impact." This often leads to a focus on the outcomes and content of transformative change, when the real focus should be on the underlying physics, as achieving transformative change depends fundamentally on the interactions of these underlying processes. The scientific challenge common to both socio-economic and hydrological systems lies in their pronounced spatio-temporal heterogeneity and variability within urban environments. This variability arises from the highly nonlinear interactions among the relevant variables, which produce extreme multiscale fluctuations and complex causal chains, beginning with the fact that responses are not proportional to the initial stimuli or forces.

Urban geosciences introduce additional complexity compared to traditional geosciences: their physical scales are much smaller, requiring not only higher-resolution observation technologies, which is already a significant challenge, but also involve much shorter interaction times. This shorter timescale is particularly crucial for prediction, as it limits the predictability of these systems. In this context, universal multifractals (multiplicative stochastic processes) likely provide the most effective framework for establishing a common foundation that supports more diverse and collectively potent approaches to transformative environmental change. Gaining a deeper understanding of multifractal phase transitions and their practical application, alongside alternative innovations, is key to fostering transformative change.

To promote such transitions, this presentation will focus on non-trivial symmetries to address much of the complexity outlined earlier. A key example is scale symmetries, which allow for the definition of scale-independent observables, in contrast to classical observables that are heavily dependent on scale. This scale dependence creates several challenges, starting with the fact that the models based on these observables are also scale-dependent. Scale-independent observables, often referred to as singularities, are significant because they capture the divergence of classical observables as resolution increases, or as we look at progressively smaller scales. The strength of this approach lies in its application to urban geosciences, specifically for: (i) defining environmental indicators for cities and their characteristics, (ii) monetizing the amenities provided by blue-green solutions in urban areas and contextualizing them socio-economically on a large scale, and (iii) developing a new form of multifractal evaluation for environmental balance - altogether enabling "transformative chift" towards the sheared value economy.

The authors sincerely acknowledge the partial financial support provided by the TIGA CfHf project (https://hmco.enpc.fr/portfolio-archive/tiga/).