Introducing the Hamiltonian as a "thermodynamic" potential

Víctor F. Correa

doi:10.1088/1361-6404/ab0e40

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arXiv · 1902.02335

Introducing the Hamiltonian as a "thermodynamic" potential

Víctor F. Correa

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Abstract

A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular velocity $\omega$, $\mathcal{H}$ is nothing but the total energy of the system plus the external actuator keeping $\omega$ fixed. In an analogy with thermodynamics, the Hamiltonian is introduced as a thermodynamic potential obtained from a Legendre transformation of the energy, in a very instructive way. The ideas can be made extensive to different problems with time-dependent constraints.

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Víctor F. Correa. 2019-02-06. Introducing the Hamiltonian as a "thermodynamic" potential. https://doi.org/10.1088/1361-6404/ab0e40

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