The closed continuous‐time homogeneous semi‐Markov system as a non‐Newtonian fluid

Abstract

The set of the attainable structures of a closed continuous-time homogeneous semi-markov system (HSMS) with n states, is considered as a continuum and the evolution of the HSMS in the Euclidean space En corresponds to its motion. In accordance with the velocity field of the HSMS, a suitable model of a continuum—defined by an acceleration-dependent stress tensor of the form T = −pI + 2μM and satisfying the Cauchy's equation of motion—is proposed in order to explain the motion of the HSMS. Then, the variation of the internal, kinetic and total energy of the model is examined. Copyright © 2000 John Wiley & Sons Ltd.