Memory in the system: trajectory-environment

TL;DR

This paper explores how memory effects arise in systems where a trajectory interacts with an environment modeled by scalar potential and noise, linking entropy, measurement, and causality in a dynamic process.

Contribution

It introduces a novel interpretation of memory as a consequence of non-elastic interactions and conformal dynamic metrics in trajectory-environment systems.

Findings

Memory emerges from non-elastic interactions.

System exhibits a transition from localization to random walk.

Memory manifests as a semi-regular drift in environmental fluctuations.

Abstract

In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the continuous "measurement" of a trajectory by an environment and\or on the contrary. In this sense the measured value is entropy-the information about embedding of the trajectory into configurations space. The concepts "measurement" and "interaction" are identified alike in quantum theory. Thus, the entropy evolution is not only the effect of dynamics, but also its cause, if it is possible to speak about causality in this case. It is shown, that such non-elastic interaction leads to occurrence of memory in the system. The reflex memory mechanism is realized as a real conformal dynamic metrics. The metastable event (attractor) is defined and time of its life is estimated. It is shown, that in the system there is a change of dynamic modes from spatial localization to random walk (fluctuation, relaxation). On scale of the attractors dynamics the memory is appearing as a semi-regular (in some information sense) drift of the image of fluctuations in a power spectrum of environment to absolute minimum. The latter properties (topological convergence) attract the attention to algorithmic aspect of a considered system.