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Multiple-relaxation-time Finsler-Lagrange dynamics in a compressed Langmuir monolayer

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.