thermodynamics - Slow thermal equilibrium

I have a question which is inspired by considering the light field coming off an incandescent lightbulb. As a blackbody radiation field, the light is in thermal equilibrium at temperature $T$, which implies that each normal mode has a mean energy given by Planck's law, and a random phase. Thus, if I were to look, microscopically, at the electric field, I would see a fairly complicated random function that can only really be considered constant at timescales $\tau\ll \hbar/k_B T$ (at which the corresponding modes have next to no amplitude and therefore do not affect the electric field's time dependence).

This illustrates a general aspect of thermal and thermodynamic equilibrium: they are only relevant concepts when the systems involved are looked at on timescales far longer than their relevant dynamics.

My question, then, is this: are examples of slowly-varying systems (where by "slowly" I mean on the timescales of seconds, or preferably longer) that can be considered to be in thermal equilibrium on timescales longer than that known?

Answer

Globular clusters are an example of such a system. Their velocity distributions are close enough to Maxwellian that, observed instantaneously, they would appear to be in thermal equilibrium unless you paid very close attention to the high velocity tail, which is truncated. Depending on the number of stars in the cluster, you may not even be able to tell this apart from shot noise in the measurement. Over longer timescales, though, the cluster is evaporating. This happens because occasionally a star will gravitationally scatter a little bit and end up on an orbit whose energy is slightly positive and escape the system. This lowers the binding energy of the system, making it easier for another star to scatter onto an orbit that lets it escape, and so on. Eventually all that is left is a pair of stars locked in a Keplerian orbit.

There are some more details on the relevant timescales in this answer, and an excellent reference on the topic is this book (chapter 7, particularly 7.5, 7.5.2). Here is some content available online that explains that GCs are well-modelled by quasi-Maxwellian distribution functions, that they can in some contexts be treated as isothermal, etc. Be warned, the rabbit hole of globular cluster dynamics is deep.