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

Integrating discrete information extracted from random process solves the impulse cutting off entropy functional (EF) measure on trajectories Markov diffusion process, integrated in information path functional (IPF). Defining the EF via the process additive functional with functions drift and diffusion allows reducing this functional on trajectories to a regular integral functional. Compared to conventional Shannon entropy measure of a random state, cutting the process on separated states decreases quantity of process information by the amount, concealed in correlation connections between these states, which hold hidden process information. The EF measure integrates information covered in both continuous process and discrete impulses. The n -dimensional process cutoff generates a finite information measure, integrated in the IPF whose information approaches the EF measure at n →∞ , restricting maximal information of the Markov diffusion process. Studied impulse delta-function cutoff and the discrete impulse deliver equivalent information at each cutoff. The constructed finite restriction limits the impulses’ discrete stepwise actions applied for cutting the regular integral on the functional increments between the cutoffs. Finite impulse step-up action transfers EF increment to following impulse whose step-down action cuts off information and step-up action starts imaginary (virtual) impulse carrying entropy increment to next real cut. Step-down cut generates maximal information while the step-up action delivers minimal information from impulse cut to next impulse step-down action. A virtual impulse transfers conjugated entropy increments during a microprocess ending with adjoining increment within actual step-down action at cutoff. Extracting maximum of minimal impulse information and transferring minimal entropy between impulses implement maxmin-minimax principle of converting process entropy to information. Each cutoff sequentially and automatically converts entropy to information, holding information Bit from random process, which connects the Bits sequences in the IPF and predicts next cut. Macroprocess, as the EF minimax extremal, integrates imaginary entropy of microprocess and cutoff information of real impulses in IPF information physical process. The EF functional measure accumulates more process information than sum of Shannon’s entropies, counted for all process’ separated states. Each EF dimensional cut measures Feller kernel information. Estimation extracting information confirms nonadditivity of the EF measured process fractions.