A Kinetic Theory Generalization of the First Law of Thermodynamics Capturing Non-Equilibrium Effects

Plasmas in many settings are out of local thermodynamic equilibrium (LTE) because the time scales for collisions to achieve LTE are longer than dynamical time scales in the plasma. Examples abound in naturally occurring and laboratory plasmas - the solar corona, interplanetary space, magnetospheres of Earth and other planets, interstellar space, compact astrophysical objects, magnetically confined fusion plasmas, high energy density plasmas, and low temperature plasmas. How energy is converted in plasmas that are not in LTE is a forefront research area across the plasma sciences, and is only well-understood for small departures from LTE. However, many plasmas can be far from LTE, and therefore a non-perturbative approach is needed. The standard approach to studying energy conversion in plasmas that can be far from LTE is to investigate changes in thermal energy and the work being done that changes the density, which are both captured by the first law of thermodynamics. In this talk, we argue that this approach omits energy conversion associated with any other higher order moments of the phase space density f, and that energy conversion associated with these moments can be important for systems far from LTE. We perform a first-principles, non-perturbative, analytic theory of the energy associated with all higher order moments of f. It is based on the concept of entropy in kinetic theory and is derived from the Boltzmann equation. We use the result to calculate energy conversion in particle-in-cell simulations of collisionless two-dimensional magnetic reconnection, which reveal that energy conversion associated with higher order moments of f can be locally significant. The theoretical results may be useful in a wide array of plasma settings.