A form of non-equilibrium statistical mechanics was developed which was designed to be applied to the evolution of dislocation structures (or patterning) during deformation. The formalism could be applied to time-independent relaxed dislocation systems as well as to time-dependent relaxation. A specific application was a simplified version of the so-called equilibrium relaxed state, for which it was shown that an effective temperature could be defined in terms of the noise in the system (back-stress fluctuations). As the noise was decreased, varying degrees of order appeared. In a second application to a simple 2-dimensional dislocation computer model, it was shown how to obtain an effective time-dependent free energy and temperature from the ensemble driving forces. Finally, it was shown that the behavior of the Boltzmann H function for the same 2-dimensional computer model could be linked to the relatively complex physics of the evolving time-dependent structure.

Non-Equilibrium Statistical Mechanics of the Evolution of Dislocation Structures. A.H.W.Ngan, R.Thomson: Physical Review B, 2007, 75[1], 014107 (11pp)