Interpretation of the Evolution of the Homogeneous Markov System (or, equivalently, of the Embedded Markov Chain) as the Deformation of a Viscoelastic Medium. The 3-D Case

Abstract

Every attainable structure of a continuous time homogeneous Markov chain (HMC) with n states, or of a closed Markov system with an embedded HMC with n states, or more generally of a Markov system driven by an HMC, is considered as a point-particle of ℜ n . Then, the motion of the attainable structure corresponds to the motion of the respective point-particle in ℜ n . Under the assumption that “the motion of every particle at every time point is due to the interaction with its surroundings”, ℜ n (and equivalently the set of the accosiated attainable structures of the homogeneous Markov system (HMS), or alternatively of the underlying embedded HMC) becomes a continuum. Thus, the evolution of the set of the attainable structures corresponds to the motion of the continuum. In this paper it is shown that the evolution of a three-dimensional HMS (n = 3) or simply of an HMC, can be interpreted through the evolution of a two-dimensional isotropic viscoelastic medium.