Journal of Physical Studies 23(3), Article 3002 [16 pages] (2019) DOI: https://doi.org/10.30970/jps.23.3002 A CLOSED DESCRIPTION OF THE NON-AUTONOMOUS DYNAMICS FOR AN ABSORBING MARKOV CHAIN WITH THREE STATES AND RANDOM TRANSITION PROBABILITIES V. I. Teslenko, O. L. Kapitanchuk Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, 14-B, Metrologichna St., Kyiv, UA-03680, Ukraine

The Tokuyama-Mori projection operator method for a closed description of averaged dynamics of a nonequilibrium subsystem weakly interacting with an equilibrium surrounding medium is applied to a non-autonomous absorbing Markov chain with three states and stochastic transition probabilities. The solution to the problem of the temporal behavior of the transient state's population is carried out in two cases for this chain, where a symmetric dichotomous stochastic process is added either to forward, or to backward transition probabilities between its states. It is shown that both solutions found are described by the generally different differential equations of the fourth order, which are complementary to each other. In the limit of the very high frequency of a stochastic process in forward/backward transition probabilities as well as in the case of a one-stage recurrent Markov chain both solutions are two-exponential and superimposed on each other. However, there is a distinction between using those solutions for the closed description of the dynamics of a two-stage absorbing Markov chain at low stochastic frequencies, in which case the former solution reveals itself as four-exponential, whereas the latter displays its effective two-exponential behavior. This indicates the existence of mutual irreducibility between the different solutions of two differential equations obtained in the general case.

PACS number(s): 02.50.Wp, 05.40.Ca, 05.70.Ln

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