Kinetic Entropy as a Diagnostic in Particle-in-Cell Simulations of Astrophysical, Heliospheric, and Planetary Plasmas.

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic electromagnetic particle-in-cell (PIC) simulations and investigate some of its uses to interpret plasma physics processes in astrophysical, heliospheric, and planetary systems. First, we calculate the kinetic entropy in two forms -- the "combinatorial" form related to the logarithm of the number of microstates per macrostate and the "continuous" form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized base simulation of anti-parallel magnetic reconnection. By decomposing the kinetic entropy into a sum of a position space entropy and a velocity space entropy, we show the velocity space entropy of both electrons and ions increases in time as the plasma heats during magnetic reconnection, while the position space entropy decreases as the plasma is compressed. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional astrophysical, heliospheric, and planetary systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks.