Evolution of the entropy across a collisionless shock

A magnetohydrodynamic (MHD) shock is a discontinuity through which plasma flows, while the mass, momentum and energy are conserved, and the entropy increases. In a collisionless system, the entropy is strictly constant along the phase-space trajectory. The MHD required entropy increase is attributed to dissipative processes causing relaxation to local thermodynamic equilibrium. The search for such dissipative processes in the shock observations usually explores variations of the entropy density or entropy per particle across the shock front. We show that both quantities may increase or decrease across the shock front even when the entropy is strictly conserved. Entropy production should be assessed using the entropy flux density.