Contact topology and non-equilibrium thermodynamics

Abstract

We describe a method, based on "hard" contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.

40 pages, 5 figures, improved exposition, mild revision of the section on Glauber dynamics

Cited by in corpus (2)

• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
• Contact geometric approach to Glauber dynamics near a cusp and its limitation