Generalized framework for characterizing entropy production in collisionless plasmas

Collisionless plasmas develop nonthermal particle distributions after being energized, and thus relax to a state of non-maximal Boltzmann-Gibbs entropy. While the Vlasov equation predicts that Boltzmann-Gibbs entropy is formally conserved (along with an infinite set of other Casimir invariants), anomalous entropy production may be enabled by phase mixing, nonlinear entropy cascades, etc. Characterizing the nature and extent of entropy production for various irreversible processes is a basic plasma physics problem with applications to space and astrophysical systems. I describe a theoretical framework for representing entropy production via an infinite set of dimensional quantities, the "Casimir momenta", which generalize the Boltzmann-Gibbs entropy and are ideally conserved by the Vlasov equation. Evolution of the Casimir momenta characterizes violations of the Vlasov equation (and therefore irreversibility) at different energy scales. The framework is validated in particle-in-cell simulations of laminar and turbulent flows. This framework may be useful for diagnosing collisionless energy dissipation and for constructing models of nonthermal particle acceleration in systems such as the solar wind and Earth's magnetosphere.