Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory

The metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory is presented, with explicit energy conservation properties and monotonic entropy production. In an axisymmetric backgroind magnetic field, the toroidal canonical angular momentum is also conserved. A new collisional current, which appears in the gyrokinetic Maxwell-Ampere equation and the gyrokinetic charge conservation law, is discussed.