The stress tensor and the energy of a continuous time homogeneous Markov system with fixed size

Abstract

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.