The differential radial flow fluctuation $v_0(p_{\mathrm{T}})$ has emerged as a new probe of the quark-gluon plasma. However, its characteristic rise-and-fall pattern with $p_{\mathrm{T}}$, resembling anisotropic flow, remains unexplained. I introduce a momentum rescaling framework that factorizes $v_0(p_{\mathrm{T}})$ into kinematic and dynamical components: $v_0(p_{\mathrm{T}})/v_0=-[d\ln ⟨n(p_{\mathrm{T}})⟩/d\ln p_{\mathrm{T}}+1]\times g(p_{\mathrm{T}})$. The first factor, determined by spectral shape, generates the rise-and-fall pattern as the spectra transition from exponential to power-law behavior. The dynamical component $g(p_{\mathrm{T}})$ isolates $p_{\mathrm{T}}$-dependent dynamics: $<1$ signals suppressed fluctuations, $>1$ indicates enhancement. Analysis of LHC data reveals $g(p_{\mathrm{T}})$ deviates from unity by 20%–40% in central collisions. Predictions for RHIC show that spectral shape alone generates the rise-and-fall baseline pattern with substantial energy dependence. This framework enables tighter medium property constraints by separating kinematic from dynamical effects, with broad applications to anisotropic flow and higher-order radial flow fluctuations.

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• Collective flow
• Particle correlations & fluctuations
• Quark-gluon plasma
• Relativistic heavy-ion collisions