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We derive and investigate several hydrodynamic formalisms that emerge from asystem of classical, ultra-relativistic scalar particles self-interacting via aquartic potential. The specific form of the total cross-section enables theanalytical computation of all transport coefficients that appear inNavier-Stokes (NS), Bemfica-Disconzi-Noronha-Kovtun (BDNK), and second-ordertransient hydrodynamic theories. We solve all these formalisms in a Bjorkenflow scenario and show that NS and BDNK theories display unphysical featureswhen gradients become sufficiently large. This implies that these hydrodynamicapproaches may not be suitable to describe the early stages of heavy ioncollisions.

Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors