Stability properties of contact structure dynamical systems

The contact structure formalism allows to model the dynamic behaviour of thermodynamic systems by means of the differential geometry. In this paper we relate the stability properties of the system to the elements of the contact structure formalism. We consider Lyapunov's first theorem to emphasize a stability criterion for the equilibrium points in terms of the system contact Hamiltonian function. This result is then related to the physical phenomena that are taking place in the system.