The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

Abstract

The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information associates with anatomy creation of impulse enables both cut entropy and stipulate random process generating information under the cut. Memory of the impulse cutting time interval freezes the observing events dynamics in information processes. Diffusion process additive functional defines EF reducing it to a regular integral functional. Compared to Shannon entropy measure of random state, cutting process on separated states decreases quantity information concealed in the states correlation holding hidden process information. Infinite dimensional process cutoffs integrate finite information in IPF whose information approaches EF restricting process maximal information. Within the impulse reversible microprocess, conjugated entropy increments are entangling up to the cutoff converting entropy in irreversible information. Extracting maximum of minimal impulse information and transferring minimal entropy between impulses implement maxmin-minimax principle of optimal conversion process entropy to information. Macroprocess extremals integrate entropy of microprocess and cutoff information of impulses in the IPF information physical process. IPF measures Feller kernel information. Estimation extracting information confirms nonadditivity of EF measured process increments.