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Renormalization group equations (RGEs) are essential for understanding scale dependence in QCD. While the DGLAP equations form the cornerstone of collider physics, modern studies of jet substructure and energy flow correlations demand a framework that extends beyond the standard DGLAP paradigm. We analytically derive a general RGE for collinear dynamics that incorporates multi-particle correlations in fragmentation at next-to-leading order, with an approach extendable to higher orders. Applying this framework, we achieve the collinear NNLL and back-to-back N4LL resummation for the energy-energy correlation on charged hadrons (tracks).