Downward Causation and Effective Potential: Rethinking Modeling Practices in Complex Systems

This paper investigates the mechanism of downward causation in emergent systems, proposing the concept of an effective potential as its mathematical formalization from the perspective of lower-level dynamics. In connection with nonlinear dynamical equations, we demonstrate that feedback mechanisms in complex systems are often erroneously reduced to phenomenological models. This reveals a methodological pitfall in physical research: phenomenological models grounded in reductionism may fail to uniquely map onto the intrinsic dynamics of the system. Consequently, we advocate establishing a new paradigm that transcends reductionism and seeks a more fundamental understanding of complex systems. Using cosmological-scale dark matter phenomena as an example, we highlight the interdisciplinary significance of this approach.