Hidden information and regularities of information dynamics IR

TL;DR

This paper introduces a novel entropy functional that uncovers hidden information in stochastic processes, revealing regularities and evolutionary dynamics beyond traditional measures, and models hierarchical information networks and their genetic codes.

Contribution

It develops an information law based on maximizing information extraction from minimal data, and introduces the information path functional for modeling process dynamics and hierarchical structures.

Findings

Reveals hidden information not captured by Shannon entropy.

Establishes an information law for process regularities.

Models hierarchical information networks and genetic codes.

Abstract

The introduced entropy functional's (EF) information measure of random process integrates multiple information contributions along the process trajectories, evaluating both the states' and between states' bound information connections. This measure reveals information that is hidden by traditional information measures, which commonly use Shannon's entropy function for each selected stationary states of the process. The hidden information is important for evaluation of missing connections, disclosing the process' meaningful information, which enables producing logic of the information. The presentation consists of three Parts. In Part 1R-revised we analyze mechanism of arising information regularities from a stochastic process, measured by EF, independently of the process' specific source and origin. Uncovering the process' regularities leads us to an information law, based on extracting maximal information from its minimum, which could create these regularities. The solved variation problem (VP) determines a dynamic process, measured by information path functional (IPF), and information dynamic model, approximating the EF measured stochastic process with a maximal functional probability on trajectories. In Part 2, we study the cooperative processes, arising at the consolidation, as a result of the VP-EF-IPF approach, which is able to produce multiple cooperative structures, concurrently assembling in hierarchical information network (IN) and generating the IN's digital genetic code. In Part 3 we study the evolutionary information processes and regularities of evolution dynamics, evaluated by the entropy functional (EF) of random field and informational path functional of a dynamic space-time process. The information law and the regularities determine unified functional informational mechanisms of evolution dynamics.