Non-thermal Statistical Mechanics of Disordered Structures and Materials

Abstract

Non-thermal Statistical Mechanics of Disordered Structures and Materials A.H.W. Ngan1 Summary When a random structure is loaded by far-field stresses, the elements inside will not be subject to the same forces because of structural inhomogeneities. Such a system represents an interesting analog to a thermal system at equilibrium – the structural irregularities qualify for a description by a Shannon-like entropy, and there is also the usual (e.g. elastic) strain energy. When an entropy is related to energy, one immediately steps into the familiar field of statistical mechanics, but for a strained random structure, the real (Kelvin) temperature plays no role. Instead, an effective temperature exists but this is not the Kelvin temperature. The proper statistical mechanics framework that should be used to describe such systems is therefore non-thermal. Using low-density elastic networks as prototype systems, this paper reviews recent computer simulation and experimental results that support such a non-thermal statistical mechanics framework. These results show the existence of an effective temperature in the description of these structures. As a second example, the dynamic formation of dislocation patterns during plastic deformation or annealing of crystals is also discussed within the same statistical mechanics framework. keywords: statistical mechanics; random materials; dislocation patterning