[kergonath]

Spin waves are similar to vibrations (phonons) in a lot of respects, you still need energy to change a spin.

That said, some aspects of thermodynamics are counter-intuitive (well, actually most of it is). Vibrations are present even at 0 K because of the uncertainty principle, and that’s true for spin waves as well as actual vibrations. It does not mean that any energy is created. The difference with time crystals is that usually these vibrations don’t involve any symmetry breaking.

Time crystals are consistent with standard thermodynamics.

[warent]

> Vibrations are present even at 0 K because of the uncertainty principle

Are you sure that's true? I can't remember the exact details but recall that being a common misinterpretation of the uncertainty principle

[kergonath]

Yes it’s true. Kinetic energy is never exactly zero, that’s called zero-point energy. Perfect stillness does not exist at the atomic scale. It would involve knowing perfectly both positions and velocities (in case of atoms, the equivalent is true for spins).

https://en.m.wikipedia.org/wiki/Zero-point_energy