Ontology of Transformation Operator in Theory of Internal Time Asymmetry of Complex Systems

Abstract

Classical methods for analyzing and evaluating the longevity indicators of mission-critical systems such as nuclear power units of nuclear power plants and icebreakers, main oil and gas pipe-lines, space stations, Earth protection systems from dangerous space objects, do not allow correctly predicting the values of longevity and safety indicators. Therefore, further studies of new theoretical methods in this area are needed. Consequently, the problem of “Time” in general and “Internal time” in particular remains extremely relevant. This article analyzes the essence of the transformation operator in the theory of asymmetry of internal time. Existing methods for assessing the asymmetry of time primarily required the development and application of operators of microscopic entropy and internal time, which have been studied deeply enough so far. The transformation operator received less attention, although its importance is very great. Hence, the purpose of this article is to generalize the achievements in evaluating the essence of the transformation operator for a problems variety of asymmetry of internal time in the past-present-future modes. To achieve this goal, the article uses the deterministic and probabilistic-statistical approaches of the theory of functional analysis operators that are already widely described in Russion and foreign literature [1–13]. The scope of existing approaches to assessing the role of the transformation operator in the theory of functional analysis operators has been expanded taking into account various asymmetries of time in the past-present-future modes.