The Homogeneous Markov System (HMS) as an Elastic Medium. The Three-Dimensional Case

Every attainable structure of the so-called continuous-time Homogeneous Markov System (HMS) with fixed size and state space S = {1, 2,…, n} is considered as a particle of R ⁿ and, consequently, the motion of the structure corresponds to the motion of the particle. Under the assumption that “the motion of every particle-structure at every time point is due to its interaction with its surroundings,” R ⁿ becomes a continuum (Tsaklidis, 1998 Tsaklidis , G. ( 1998 ). The continuous time homogeneous Markov system with fixed size as a Newtonian fluid? Appl. Stoch. Mod. Data Anal. 13 : 177 – 182 .Crossref] , Google Scholar]). Then the evolution of the set of the attainable structures corresponds to the motion of the continuum. For the case of a three-state HMS it is stated that the concept of the two-dimensional isotropic elasticity can further be used to interpret the three-state HMS's evolution.