Variational construction of connecting orbits between Legendrian graphs
Liang Jin, Jun Yan, Kai Zhao
TL;DR
This paper introduces a variational method for constructing connecting orbits between Legendrian graphs in contact Hamiltonian systems, inspired by Aubry-Mather and weak KAM theories, with implications for thermodynamic stability.
Contribution
It develops a novel variational framework for connecting orbits between Legendrian graphs, extending Aubry-Mather and weak KAM theories to contact Hamiltonian systems.
Findings
Provides mechanisms for constructing semi-infinite orbits
Links thermodynamic stability with geometric structures
Extends variational methods to contact systems
Abstract
Motivated by the problem of global stability of thermodynamical equilibria in non-equilibrium thermodynamics formulated in a recent paper [12], we introduce some mechanisms for constructing semi-infinite orbits of contact Hamiltonian systems connecting two Legendrian graphs from the viewpoint of Aubry-Mather theory and weak KAM theory.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Control and Stability of Dynamical Systems · Quantum chaos and dynamical systems