Timeline for When is the Hamiltonian of a system not equal to its total energy?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 21 at 15:27 | comment | added | Michael Levy | This is a great second example. How would it be for you to add this to your existing post? It would round out your ideas substantially in my humble opinion | |
| Oct 21 at 15:25 | comment | added | Ján Lalinský | @MichaelLevy Yes, I think everybody will agree that damped oscillator is a model of a dissipative system, because kinetic plus potential energy decreases in time. The interpretation that this energy dissipates into environment is not part of the model, but we usually think about damped oscillator in such a way that energy does not just disappear, but goes into environment, hence "dissipation". $H$ is not necessarily energy in general, not just in case of energy decreasing to zero.There is another such example, involving Hamiltonian description in a rotating frame,where again $H$ is not energy. | |
| Oct 21 at 15:21 | comment | added | Ján Lalinský | @RyderRude No, it is the Hamiltonian which is a "generator of time translations". Energy has many forms and many definitions. In mechanics, energy is T+U, sum of kinetic and potential energy. Hamiltonian need not have this value. | |
| Oct 21 at 15:10 | comment | added | Michael Levy | This indeed is an example of Hamiltonian that is NOT equal to the total energy of a system. Correct me if I am wrong, but the physical interpretation would have to be that the example herein is a dissipative system. The inference might be that for dissipative systems in general, the Hamiltonian is not equal to the total energy. | |
| Feb 9 at 19:37 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
added 117 characters in body
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| Sep 29, 2023 at 14:09 | comment | added | Ryder Rude | I thought energy was simply the generator of time translations (which would make it the Noether charge of time symmetry and undefined when there is no time symmetry). Is this not the general definition of energy? | |
| Feb 15, 2021 at 18:00 | history | answered | Ján Lalinský | CC BY-SA 4.0 |