  The relaxation of magnetically confined plasmas in a toroidal geometry is
analyzed. From the equations for the Hermitian moments, we show how the system
relaxes towards the mechanical equilibrium. In the space of the parallel
generalized frictions, after fast transients, the evolution of collisional
magnetically confined plasmas is such that the projections of the evolution
equations for the parallel generalized frictions and the shortest path on the
Hermitian moments coincide. For spatially-extended systems, a similar result is
valid for the evolution of the {\it thermodynamic mode} (i.e., the mode with
wave-number k = 0). The expression for the affine connection of the space
covered by the generalized frictions, close to mechanical equilibria, is also
obtained. The knowledge of the components of the affine connection is a
fundamental prerequisite for the construction of the (nonlinear) closure theory
on transport processes.
