The observable $v_0\left(p_{\mathrm{T}}\right)$, which quantifies event-by-event fluctuations of the differential transverse-momentum spectrum, has been proposed as a direct and sensitive probe of radial flow in heavy-ion collisions. Recent measurements at the CERN Large Hadron Collider exhibit a clear mass ordering for pions, kaons, and protons at low $p_{\mathrm{T}}$ and a baryon-meson splitting at intermediate $p_{\mathrm{T}}$, resembling the well-known features of elliptic flow $\left(v_2\right)$. In this work, we first derive an analytic expression for $v_0\left(p_{\mathrm{T}}\right)$ within a blast-wave framework that incorporates fluctuations of the freeze-out temperature and radial expansion velocity, and we show that this formulation naturally explains the experimentally observed mass ordering. Furthermore, within a quark coalescence picture, supported by transport simulations using A Multi-Phase Transport model, we demonstrate that the baryon-meson splitting at intermediate $p_{\mathrm{T}}$ emerges dynamically from partonic $v_0\left(p_{\mathrm{T}}\right)$. This study provides deeper insight into the $v_0\left(p_{\mathrm{T}}\right)$ observable and the collective dynamics of the quark-gluon plasma.

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• Collective flow
• Relativistic heavy-ion collisions