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

TL;DR

This paper models the first-order phase transition in Langmuir monolayers using an information geometric approach with Finsler-Lagrange dynamics, highlighting the role of relaxation times and electrocapillary forces.

Contribution

It introduces a novel Finsler-Lagrange geometric framework to describe phase transitions in monolayers, incorporating multiple relaxation times and electrocapillary effects.

Findings

Geodesic trajectories can contract or spread, indicating phase transition dynamics.

The Finsler-Lagrange framework effectively models the information geometrodynamics of the transition.

Electrocapillary forces act as information constraints on the statistical manifold.

Abstract

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.