Ervin Goldfain. Introduction to Complex Dynamics of Non-equilibrium Systems
Natural Sciences / Physics / Mathematical Physics
Submitted on: Apr 20, 2026, 10:55:00
Description: Complex dynamics (CDYN) is present across many fields of human activity, from physics, social sciences, political and financial affairs, to biology, geophysics, internet traffic, weather forecasting and cosmology. It exhibits robust large-scale regularities despite operating in a diversity of contexts. This paper unveils a unified framework for describing CDYN, based on non-equilibrium statistical physics. Emphasis is placed on the role of continuous and scale-dependent dimensions, anomalous transport, generalized entropies, and Renormalization Group (RG) flows in organizing macroscopic behavior. We argue that complexity is not an emergent accident but the natural outcome of systems operating near critical manifolds in phase space, often maintained through self-organized criticality (SOC). The paper introduces a lexicon of foundational concepts to standardize language across disciplines and prepare the ground for a systematic theory of CD applicable primarily to field theory and cosmology.