Degree of Order Criteria of the Elements’ Deterministic Chains With Relations Between the Closest Neighbors

Abstract

For the first time ever, this work formulates definition of the degree of order for the non-random sequence of elements. Earlier, the only known parameter to evaluate a system’s degree of order was entropy. It has been shown that using entropy to evaluate the degree of order in deterministic chains of elements leads to a contradiction. Words built out of k different elements are being considered. Compositions are built from a random number of closed words that in total contain an equal quantity of each of the k elements. Hereby a new approach is being offered for the degree of order definition based upon comparison of the given composition with a high-symmetry word composition. Composition is described by means of the matrix of the number of pairs, in which the sum of elements in each line and each column are equal. Features of the pair matrix are studied. Pair matrices are expanded into the matrices of ideal states that describe compositions of words with shift symmetry. By means of this expansion the degree of order had been defined and its combinatory meaning had been revealed. A model of the ”cybernetic bug”, able to cut words in certain places, had been studied. It had been shown that repeated attacks by this cybernetic bug together with subsequent random patching of the cut words may, in a relatively short period of time, transfer composition to the ideal state.