Irreversibility and entropy issues concerning the heating of directly transmitting ions at low Mach number perpendicular collisionless shocks

In a previous paper the authors analysed a simple model accounting for the anisotropic temperature increase that occurs to ions at collisionless, low Mach number shocks. While a complete closed form solution for the particle distribution in phase space is not possible, many basic properties of the distribution were proved. In this paper, we apply these insights to a discussion of the thermodynamic issues: in particular the thermodynamic temperature, the adiabatic (in the thermodynamic sense) nature of the heating and the entropy. We examine how the anisotropic temperature distribution stores reversible work, and show how the entropy associated with the temperature increase at the shock remains constant prior to thermalisation.