  A redefinition of the Lagrangian of a multi-particle system in fields
reformulates the single-particle, kinetic, and fluid equations governing fluid
and plasma dynamics as a single set of generalized Maxwell's equations and
Ohm's law for canonical force-fields. The Lagrangian includes new terms
representing the coupling between the motion of particle distributions, between
distributions and electromagnetic fields, with relativistic contributions. The
formulation shows that the concepts of self-organization and canonical helicity
transport are applicable across single-particle, kinetic, and fluid regimes, at
classical and relativistic scales. The theory gives the basis for comparing
canonical helicity change to energy change in general systems. For example, in
a fixed, isolated system subject to non-conservative forces, a species'
canonical helicity changes less than total energy only if gradients in density
or distribution function are shallow.
