  In this paper, we present a new framework for addressing the nonlinear Landau
collision operator in terms of particle-in-cell methods. We employ the
underlying metriplectic structure of the collision operator and, using a macro
particle discretization for the distribution function, we transform the
infinite-dimensional system into a finite-dimensional time-continuous
metriplectic system for advancing the macro particle weights. Temporal
discretization is accomplished using the concept of discrete gradients. The
conservation of density, momentum, and energy, as well as the positive
semi-definite production of entropy in both the time-continuous and the fully
discrete system is demonstrated algebraically. The new algorithm is fully
compatible with the existing particle-in-cell Poisson integrators for the
Vlasov-Maxwell system.
