Hidden stochastic, quantum and dynamic information of Markov diffusion process and its evaluation by an entropy integral measure under the impulse controls actions, applied to information observer

TL;DR

This paper explores how impulse interactions with Markov diffusion processes reveal hidden information through entropy cutting, leading to a new entropy integral measure for evaluating information micro and macro processes in dynamic systems.

Contribution

It introduces a novel entropy integral measure based on impulse actions to evaluate hidden information in Markov diffusion processes and models the micro-macro information dynamics.

Findings

Impulse actions reveal hidden information by cutting correlations.

Entropy integral measure quantifies information flow along diffusion trajectories.

Micro and macro processes are described by extreme equations derived from variation principles.

Abstract

Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy. Each inter action models Kronicker impulse, delta impulse models interaction between the Kronicker impulses. Each impulse step down action cuts maximum of impulse minimal entropy and impulse step up action transits cutting minimal entropy to each step up action of merging delta function. Delta step down action kills delivering entropy producing equivalent minimax information. The merging action initiates quantum microprocess. Multiple cutting entropy is converting to information micro macroprocess. Cutting impulse entropy integrates entropy functional EF along trajectories of multidimensional diffusion process. Information which delivers ending states of each impulse integrates information path functional IPF along process trajectories. Hidden information evaluates Feller kernel whose minimal path transforms Markov transition probability to probability of Brownian diffusion. Each transitive transformation virtually observes origin of hidden information probabilities correlated states. IPF integrates observing Bits along minimal path assembling information Observer. Minimax imposes variation principle on EF and IPF whose extreme equations describe observing micro and macroprocess which describes irreversible thermodynamics. Hidden information curries free information frozen from correlated connections. Free information binds observing micro macro processes in information macrodynamics. Each dynamic three free information composes triplet structures. Three structural triplets assemble information network. Triple networks free information cooperate information Observer.