Exploring emergence from the perspective of Langevin-type growth theory

Emergence is a fundamental characteristic of complex systems, often used to describe phenomena that cannot be accounted for through reductionist approaches. In the field of surface growth dynamics, long-range correlations have been shown to disrupt self-affine structures, resulting in anomalous scaling that remains unexplained by the underlying mechanisms. In this paper, we adopt two independent quantitative measures of emergence, namely the Hellinger distance and novelty detection, to investigate the peculiar phenomena from the perspective of Langevin-type growth theory. Our results demonstrate that the incorporation of long-range temporal correlations and deterministic terms can give rise to emergent behaviors in the Langevin-type growth systems, such as the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) equations. In contrast, the purely random growth (RG) equation, which lacks deterministic terms, fails to exhibit emergent phenomena even in the presence of strong temporal correlations. This work provides new insights into the physical mechanisms underlying emergent phenomena in complex natural systems. By linking long-range correlations and deterministic dynamics to emergence, our findings also relate to contemporary multifractal and cascade-based perspectives. Furthermore, this integration contributes to a unified theoretical framework for identifying the universal principles of emergence that govern both living and non-living complex systems.