Authors: M. Hasan Barbhuiya (West Virginia University), Paul Cassak (West Virginia University), Haoming Liang (The University of Alabama at Huntsville), and Matthew Argall (University of New Hampshire)

Kinetic-scale energy conversion and dissipation play a crucial role in the dynamics of turbulence and magnetic reconnection in space plasmas. In the collisionless regime, kinetic effects can result in strongly non-Maxwellian distribution functions, meaning the plasma is far from local thermodynamic equilibrium (LTE). Recently, the non-LTE contributions to plasma heating or cooling have been extensively studied, via particle-in-cell simulations of turbulence and reconnection, and satellite observations through the “Pi-D” parameter [Y. Yang et al., Phys. Plasmas, 24, 072306 (2017)]. We note that the time evolution equation for the plasma temperature can be reinterpreted as a “non-LTE generalization” of the first law of thermodynamics. In the present study, we show how this equation is incomplete because it only captures compressive work which is the change in the number density (zeroth moment of the phase space density), and Pi-D and heat flux which accounts for changes to temperature (second moment), but it is agnostic to changes to Pi and higher-order moments. Using entropy defined in kinetic theory, we derive an equation to describe these manifestly non-LTE kinetic effects and show that it supplants the first law of thermodynamics – we dub it “the first law of kinetic theory.” We show how it describes energy conversion to changes in any moment of the phase space density, not just the number density and temperature, thus describes arbitrary evolution of the shape of the phase space density. We introduce a new measure on the same footing as Pi-D and the vector heat flux divergence dubbed “higher-order non-equilibrium term” (HORNET) which quantifies energy conversion to Pi and higher moments of the phase space density. We conclude with results from particle-in-cell simulations of symmetric magnetic reconnection comparing amplitudes and profiles of terms in the first law of kinetic theory and HORNET.