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Journal of Physical Studies 19(1/2), Article 1001 [10 pages] (2015)
DOI: https://doi.org/10.30970/jps.19.1001 DEFINING COMPETITIVITY OF AN ABSORBING MARKOV CHAINV. I. Teslenko1, O. L. Kapitanchuk2
Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, |
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The problem of defining the competitivity for the different states of an absorbing Markov chain is formulated in a continuous time framework. Chain states are associated with the modules of locally equilibrated, fluctuating energy levels formed due to strong adiabatic interactions within a nonequilibrium system being nonadiabatically coupled weakly to the equilibrium environment. Using a microscopic approach to the description of time evolution of the density matrix of the whole system, we first reduce the corresponding Liouville-von Neumann equation to a master equation for diagonal elements of the density matrix of a nonequilibrium system, then provide a calculus of involved chaotic and stochastic averages with the supposed initial and completed energy-level distributions, and finally arrive at the kinetic equation for the population of aggregated chain states. The equation is in detail balanced by respective transition probabilities being well defined for all the differences between energies and dimensionalities of the chain state modules. For the case of an absorbing Markov chain, this makes it possible to define the competitivity for different modular states, as an inverse slope of log odds of normalized peaks of their population with respect to log of various input transition probabilities set to be free in the wide limits.
PACS number(s): 05.70.Ln, 02.50.Ga, 05.40.-a