I study the event-by-event fluctuation and rapidity decorrelation of the mean transverse momentum $\left[p_T\right]$, which has recently been proposed as a sensitive probe of the equation of state at finite baryon density. The investigation reveals that, in a baryon-rich medium, the event-by-event fluctuation of the mean transverse momentum is driven by the combined effects of energy-density and net-baryon-density fluctuations. Consequently, the rapidity dependence of this observable provides a promising handle to probe the three-dimensional structure of both energy and baryon density profiles. Previous studies have shown that $\left[p_T\right]$ decorrelation with rapidity is largely insensitive to shear and bulk viscosity; however, its dependence on baryon diffusion, another key transport coefficient in baryonic matter, has not been explored. I find that baryon diffusion has a negligible impact, establishing this observable as a robust probe of the equation of state. Furthermore, I present predictions for identified hadrons and observe a pronounced splitting in the rapidity decorrelation of mean transverse momentum between protons and antiprotons, indicating different transverse flow dynamics for baryons and antibaryons.

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