Breakdown of Hydrodynamics in a Simple One-Dimensional Fluid

TL;DR

This paper reveals that in a one-dimensional diatomic fluid, shock wave behavior defies traditional hydrodynamic predictions, showing persistent non-equilibrium features and algebraic relaxation, challenging existing theoretical models.

Contribution

It demonstrates the breakdown of hydrodynamic and kinetic theories in describing shock waves in 1D fluids, highlighting persistent non-equilibrium phenomena and multiscaling effects.

Findings

Shock wave properties differ from hydrodynamic predictions.

Non-equilibrium effects decay algebraically with distance.

Velocity distribution moments exhibit multiscaling.

Abstract

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches, e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Non-equipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1d fluids.