Phase transitions in one-dimensional mechanical models of thermodynamics and the physics of the Hall bar system

We study one- dimensional mechanical systems by using a thermodynamic approach. In this framework we discuss the appearance of distinct thermodynamic phases corresponding to different types of trajectories for a charge carrier moving in a Hall bar, i.e.a channel patterned in a two-dimensional electron gas subject to a transverse magnetic field. In this device different kinds of orbits are allowed, cyclotron orbits, skipping orbits (when the particle collides with one channel wall), and traversing trajectories (when the particle collides with both channel walls).The passage from one type of orbits to the other can be characterized as a phase transition; so, in this system two different phase transitions can be identified.