We explore theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions by examining the full non-linear causality conditions and quantifying the second-order transport coefficients role on flow observables. The causality conditions impose physical constraints on the maximum allowed values of inverse Reynolds numbers during the hydrodynamic evolution. Including additional second-order gradient terms in the Denicol-Niemi-Moln{a}r-Rischke (DNMR) theory significantly shrinks the casual regions compared to those in the Israel-Stewart hydrodynamics. For Au+Au collisions, we find the variations of flow observables are small with and without imposing the necessary causality conditions, suggesting a robust extraction of the Quark-Gluon Plasmas transport coefficients in previous model-to-data comparisons. However, sizable sensitivity is present in small p+Au collisions, which poses challenges to study the small systems collectivity.
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