Deterministic shock wave gas dynamics: force balance, phase space quantization and mesoscopic degradation criterion

Abstract (Description):This paper presents a rigorous derivation of the governing equations for a steady one-dimensional shock wave based on extended anisotropic thermodynamics and deterministic gas dynamics. Unlike the classical Rankine-Hugoniot jump theory, which relies on the statistical Maxwell-Boltzmann velocity distribution, this approach is founded on direct force balance, phase space quantization along six orthogonal directions (the sweeping cylinders method), and Gert's generalized adiabatic index. An analytical expression for the gas compression ratio across the wave front is obtained, and a fundamental kinetic criterion for wave stationarity is derived. It is demonstrated that shock wave degradation and its degeneration into a regular acoustic wave occur when the front velocity drops below a critical threshold. Below this threshold, the translational kinetic energy of the particles ceases to exceed the potential interaction energy of their electron shells, triggering a reverse mesoscopic phase transition and the reassembly of elastic molecular chains. Furthermore, it is shown that under supercritical temperature regimes, where potential bonds between electron shells are completely broken by thermal motion, the propagation of classical sound waves is impossible, and all wave disturbances are governed exclusively by the derived shock transfer equations. this is the English version of the main article