Multiple-Relaxation-Time Finsler-Lagrange Dynamics in a Compressed Langmuir Monolayer

Abstract

We propose an information geometric approach to describe the emergence of transient and metastable states in a compressed monomolecular layer (monolayer) of amphiphilic molecules on the air/water interface. Using a statistical manifold formed by microscopic states with a large number of relaxation times, a simulation of the entropy evolution of the structurizing monolayer has been performed. The electrocapillary forces are considered as information constraints on the statistical manifold. The Jacobi stability analysis shows that the information geometrodynamics of the statistical manifold for a first-order phase transition in the Langmuir monolayer is of Finsler-Lagrange type.