The engineering community has been actively pursuing the development of self-organization of particles in order to design smaller, faster and more efficient electronic elements. In order to achieve theoretical understanding of these processes, we suggest a dissipative analogue of kinetic equations that describe the motion of probability distribution in the momentum-coordinate space. This work is based on the double bracket dissipation ideas that were originally suggested for astrophysical applications.

We then show how to extend the double bracket method to include particles with interaction dependent on orientation, for example, magnetized particles in colloidal solution. We derive evolution equations for density and magnetization that reduce to the celebrated Landau-Lifshitz-Gilbert equations for non-moving magnets and to Debye-Huckel equations for particles without orientation. We also show how our equations naturally give the motion for of an elastic self-interacting curve, and discuss the application of our technique to folding of biologically-relevant strands.

Collaborators: Darryl D. Holm, Cesare Tronci (Mathematics, Imperial College, London