Phase Transition in Extended Thermodynamics Triggers Sub-shocks

Extended thermodynamics commonly uses polynomial moments to model non-equilibrium transportation, but faces a crisis due to sub-shocks, which are anomalous discontinuities in gas properties when predicting shock waves. The cause of sub-shocks is still unclear, challenging the validity of extended thermodynamics. This paper reveals, for the first time, that sub-shocks arise from intrinsic limitations of polynomials leading to a discontinuous phase transition. Therefore extended thermodynamics necessitates alternative moments beyond polynomials to avoid sub-shocks.