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Stephen Hawking stated that the 21st century would become the century of complexity. Physics approaches have increasingly contributed to a deeper understanding of emerging phenomena from fundamental microscopic interactions not just in quantum mechanics, particle physics or gravitational theory. Combining tools from statistical physics, nonlinear dynamics, and network science also provides insights into pattern formation processes, universal scaling, and phase transitions in complex biological or social systems. Human mobility is a prototypical example of such a complex system, characterized by simple interactions between a large number of individual participants. Here, insights into the collective dynamics have helped, for example, to explain the emergence of congestion waves in car traffic. Today, new modes of mobility promise more sustainable and accessible mobility. However, as mobility services become more interconnected and complex, new collective states emerge that may be detrimental to their function. A statistical physics approach to these systems enables us to understand the fundamental mechanisms underlying the collective dynamics and thus helps predict and design sustainable mobility systems. In this talk, I will present two current examples that highlight the potential of statistical physics and complex systems analysis in the context of mobility: the emergence of unintended collective states from dynamic pricing mechanisms and universal scaling in the dynamics of ride-sharing fleets.

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