Universal Equations of Self-Organization in Non-Equilibrium Complex Systems: Rough Operator Algebra and Composite Torsion in Phase Space

Traditional non-equilibrium thermodynamics, grounded in local equilibrium and linear response frameworks, fails to fully characterize far-from-equilibrium complex systems where fluctuations act as the primary driving force of macroscopic order. In this paper, we establish a universal mathematical framework for self-organization by integrating Rough Operator Algebra (ROA) and Composite Torsion within phase space. We demonstrate that the noncommutativity of microscopic rough operators generates non-vanishing commutators that act as topological triggers for symmetry breaking and macro-collapse into stable attractors.