  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.
