Canonical ensemble for static elastic structures with random microstructures

A constant-(N,V,T,θ) ensemble is proposed to describe the elastostatics of random solid structures. Within the harmonic approximation, the energy of such a solid structure is the sum of a thermal and a strain component without mutual interaction. Systems in this ensemble thus draw energies from two separate baths: one thermal and the other mechanical. A mechanical entropy and an effective temperature (θ) can then be defined on the same rigorous basis as the thermal entropy and the Kelvin temperature (T). This ensemble approach can be used to calculate the properties of solid structures sharing similar microstructural randomness.