Non-Markov Stationary Time Correlation in Complex Systems with Discrete Current Time

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.