Vladimir S. Lerner

The introduced entropy integral measure on random trajectories (EF) is defined by the process additive functional with functions drift and diffusion reducing this functional on trajectories to a regular integral functional. This functional evaluates the cutting process impulses imposed through an impulse control.

The impulse control cuts the process EF on elementary information impulse which the introduced information path functional (IPF) integrates in a bit composing an information process.

Compared to 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 a hidden process information infinite.

The impulse elementary interactive cutting action provides both reduction of the observing process entropy and discrete unit of the cutting entropy memorized as an information Bit.

That defines information as memorized entropy cutting in random observations which process interactions.

Cutting maximum of minimal impulse information and transferring minimal entropy between impulses implement the paper maxmin-minimax principle of converting process entropy to information. Each cutoff sequentially and automatically converts entropy to information, naturally encoding information Bit from random process, which connects the Bits sequences in the IPF, and the EF predicts next cut.

The impulse curvature, enclosing the entropy of interacting impulses, enables converting inner energy of an external (natural) process to bit of the interacting process which memorizes the bit by delivering the Landauer energy. It allows encoding the IPF information in evolving natural code.

We found the conditions creating a natural bit memorized in interacting curved impulse and the conditions generating a code of the interacting information process which assembles the natural bits.

The natural encoding satisfied Landauer’s principle and compensates for the cost of Maxwell’s Demon.

The energy of a specific interaction limits the universal code length and density.

It is shown that each IPF dimensional cut measures Feller kernel information.

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.

Estimation extracting information confirms non-additivity of the EF measured fractions.

The multiple applications validate the results.