An Interdisciplinary Journal

* 2001, Volume 4, Number 4, pp.412-423*

The statistical non-Hamiltonian theory of fluctuation in the complex systems
with a discrete current time is presented. Quasidynamic Liouville equation for
the
state vector of the complex system serves as a initial point of the discrete
analysis.
The projection operator in a vector state space of finite dimension allows to
reduce
Liouville equations to a closed non-Markov kinetic equation for a discrete time
correlation function (TCF). By the subsequent projection in the space of
orthogonal
variables we found a discrete analoguos of famous Zwanzig-Mori's equations for
the
nonphysical non-Hamiltonian systems. The main advantage of the finite-difference
approach developed is served with two moments. At first, the method allows to
receive discrete memory functions and statistical spectrum of non-Markovity
parameter for the discrete complex systems. At second, the given approach allows
to
plot a set of discrete dynamic information Shannon entropies. It allows
successively
to describe non-Markov properties and statistical memory effects in discrete
complex
systems of a nonphysical nature

*Key words: *non-Markov discrete processes, finite-discrete
kinetic equations, memory functions, dynamical Shannon entropy

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Last updated: *October 15, 2001*