Kinetic Entropy as a Diagnostic in Particle-in-Cell Simulations

While entropy has been used broadly in fluid and gyrokinetic models, kinetic entropy of fully kinetic plasma systems has been vastly under-utilized. It is the natural metric of irreversible dissipation since it is conserved in ideal closed systems and increases when there is dissipation. This suggests kinetic entropy can address important questions on the nature of dissipation. In this work, we carry out an initial study to develop the diagnostic in collisionless particle-in-cell (PIC) simulations, using 2.5 D anti-parallel reconnection as a test case.  First, we calculate the traditional kinetic entropy and the full Boltzmann entropy.  We show kinetic entropy can be decomposed into a sum of a velocity space and position space entropies. We find that total entropy in the simulations is preserved quite well - within two percent - and use the departure from conservation to quantify the effective numerical dissipation. Finally, we use kinetic entropy to identify regions with non-Maxwellian distributions and compare it to other approaches including J dot E', agyrotropy, and Pi-D.  The infrastructure developed here will be useful for studies of weakly collisional systems, including reconnection, turbulence and shocks, and is being applied to Magnetospheric Multiscale (MMS) data.