  In this paper an information geometric approach has been proposed to describe
the two-dimensional (2d) phase transition of the first order in a monomolecular
layer (monolayer) of amphiphilic molecules deposited on air/water interface.
The structurization of the monolayer was simulated as an entropy evolution of a
statistical set of microscopic states with a large number of relaxation times.
The electrocapillary forces are considered as information constraints on the
statistical manifold. The solution curves of Euler-Lagrange equations and the
Jacobi field equations point out contracting pencils of geodesic trajectories
on the statistical manifold, which may change into spreading ones, and
converse. It was shown that the information geometrodynamics of the first-order
phase transition in the Langmuir monolayer finds an appropriate realization
within the Finsler-Lagrange framework.
