Entropy generation at multi-fluid magnetohydrodynamic shocks with emphasis to the solar wind termination shock

In a series of earlier papers, we developed expressions for ion and electron velocity distribution functions and their velocity moments at the passage over the solar wind termination shock. As we have shown there, with the introduction of appropriate particle invariants and the use of Liouville's theorem one can get explicit solutions for the resulting total downstream pressure by adding up from partial pressure contributions of solar wind protons, solar wind electrons and pick-up protons. These expressions are the first step toward delivering the main contributions to the total plasma pressure in the downstream plasma flow and consistently determine the shock compression ratio. Here we start from these individual fluid pressures downstream of the shock and thereafter evaluate for the first time the shock-induced entropy production of the different fluids, when they are passing over the shock to the downstream side. As shown here, the resulting ion entropy production substantially deviates from earlier calculations using a pseudo-polytropic reaction of the ions to the shock compression, with polytropies selected to describe fluid-specific reactions at the shock passage similar to those seen by the Voyagers. From these latter models, ion entropy jumps are derived that depend on the pick-up ion abundance, while our calculations deliver an abundance-independent ion entropy production that only depends on the shock compression ratio and the tilt angle between the upstream magnetic field and the normal to the shock surface. We also show here that the thermodynamically permitted upper limit in the entropy production is only reached when strongly heated electrons are included in the entropy balance.