The Vlasov equation cannot fully account for collisionless shocks

TL;DR

The paper argues that the Vlasov equation is insufficient for modeling collisionless shocks because it conserves entropy, unlike shocks which involve entropy changes, suggesting the need for a more detailed kinetic theory.

Contribution

It highlights the limitations of the Vlasov equation in describing collisionless shocks and proposes that a more rigorous approach at the Klimontovich level may be necessary.

Findings

Vlasov equation conserves entropy during shock processes

Collisionless shocks involve entropy changes not captured by Vlasov

A rigorous theory may require Klimontovich-level modeling

Abstract

It is argued that the Vlasov equation cannot fully account for collisionless shocks since it conserves entropy, while a shock does not. A rigorous mathematical theory of collisionless shocks could require working at the Klimontovich level.