Statistical Physics Approaches to Low-Speed Human Movement

Collective human movement is a hallmark of complex systems, showing emergent structure in settings from pedestrian crowds to biological swarms. In low-speed, socially engaged motion, alignment reflects interpersonal interaction rather than navigation. This dissertation examines this regime using multimodal sensing in preschool classrooms, combining high-resolution ultra-wideband tracking, body-orientation data, and child-worn audio.

We identify a sharp, distance-dependent transition in alignment: children align side-by-side within 0.65 m and face-to-face at larger distances, indicating spontaneous symmetry breaking between social phases. A Fourier decomposition of orientation distributions shows that this arises from distance-dependent competition among three mechanisms, parallelization, opposition, and reciprocation. A minimal pseudo-potential model reproduces empirical alignment distributions through Monte Carlo simulations, demonstrating that this transition is a non-equilibrium phase transition in social orientation dynamics.

We also analyze the dyadic structure of vocal interactions. Audio data show that vocalization is co-regulated within pairs, not an individual trait. A minimal two-state model of vocal engagement captures partner-driven responsiveness across both neurotypical children and children with developmental differences, highlighting the primacy of the dyad in early language behavior.

Together, these results establish a quantitative framework for low-speed human alignment, linking statistical physics, active matter, and developmental science. Integrating spatial, orientational, and vocal modalities, this work advances theoretical, empirical, and methodological approaches to socially mediated human behavior, with implications for learning environments, developmental interventions, epidemic modeling, and artificial collectives.