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Thermodynamics and equilibrium statistical mechanics describe states that are global minima of free energies, and are independent of time.But this is like a map showing only cities, without the roads connecting them.How do we describe the roads to re-equilibration?
We consider three-valued pseudospin variables interacting via powerlaw anisotropic interactions, describing discretized elastic strains of unit cells undergoing a solid-solid structural phase transition. The powerlaw comes from a no-defect 'compatibility' constraint. The slow variables in the system are strain domain walls, separating the competing low-temperature crystal structures.
Monte Carlo simulations show *slow* domain wall re-equilibrations, after a temperature quench across the transition temperature.
Activated time delays from jumps over energy barriers are familiar. Here, we have non-activated *entropy barriers* from searches for rare pathways to the equilibrium state. We identify the rare pathways in detail, and the divergence of entropy barriers,
that leave the system trapped in the starting state.
The ideas may have relevance for the long-standing problem of configurational glasses. |