  Motivated by explosive releases of energy in fusion, space and astrophysical
plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic
(MHD) equilibria against interchanges of straight magnetic-flux tubes. We
demonstrate that in MHD (unlike in hydrodynamics) linear stability does not
guarantee nonlinear stability, even in this simple case. We show that the
minimum-energy configurations attainable by metastable equilibria under
non-diffusive 2D dynamics can be determined by solving a combinatorial
optimization problem. These minimum-energy states are, to good approximation,
the final states reached by simulations of destabilized metastable equilibria
where turbulent mixing is suppressed by viscosity. For the case of fully
turbulent relaxation, we construct a statistical mechanical theory based on the
maximization of Boltzmann's mixing entropy. This theory is analogous to the
Lynden-Bell statistical mechanics of stellar systems and collisionless plasmas
and to the Robert-Sommeria-Miller (RSM) theory of 2D vortex turbulence. Our
theory reproduces well the results of our numerical simulations for
sufficiently large perturbations to the metastable equilibrium.
