Entropy of microstructure

Two points are made in this paper: first, energy of random structures is not determined uniquely by any finite set of the characteristics of microstructure. The information lost is characterized by entropy of microstructure; it describes the scattering of the values of energy. Therefore, entropy of microstructure is a key thermodynamic parameter in phenomenological modeling of the behavior of random structures. Second, mathematical modeling of a random structure is based on the construction of its probabilistic measure; a way to select the probabilistic measure from the experimental data is outlined. The corresponding probabilistic measure is remarkably similar to that of classical statistical mechanics, though the underlying physics is quite different. After the probabilistic measure is chosen, the entropy of microstructure can be found from the analysis of the homogenization problem. Entropy of microstructure is computed in two example problems. Applications to phenomenological modeling of work hardening are discussed.