Minimal Mechanical Model of Thermodynamics

In this chapter we shall see how the conservative character of the thermodynamic field, hence the existence of a thermodynamic potential, emerges from the very Hamiltonian nature of the equation of motion in the case of a particle in a U-shaped potential. This result is known as the Helmholtz theorem. We shall illustrate this with the most minimal mechanical model of a thermodynamic system, namely a particle in a 1D box, and other examples.