Effect of Subsystems Information Feedback on the Entropy of the Whole System. Part Ii. Transformation Schemes of Distinct Information Chains

摘要

This report represents the transformation schemes of an information system not connected directly with any particular physical system. In the present scheme the number of subsystems is unlimited, and the number of states is arbitrary. A transformation of the system from one state to another is not connected with any physical phenomenon. The transformations of the entire system are arranged in a state-wise manner. All the additional operations such as regrouping, reordering, renormalization, and calculation of the sensitivity coefficients have to be performed between the particular states of the transformations of the entire system. For illustrative purposes, it is assumed that the information system consists of four subsystems, S1 to S4, each containing a certain number of distinct parameters together with a set of probabilities associated with each parameter. The probabilities are normalized to unity. After the initial state is closed, there takes place the transformation of the entire information system from S(0) to S(1). The transformation is a momentary process. The number of subsystems in S(1) does not necessarily need to be equal to the total number of subsystems. In the present scheme of the transformations it is necessary to record continuously, after each state, the past history of each parameter independently of the formalism of transformations. The parameters are shifted from one subsystem to another, and in their symbolic notations the origin of the parameter and its destination are not marked. The recording of the history of each parameter is an important item. This report presents the formalism of four transformation states. (Author)