I would like to understand if it is possible to perform an experiment, where a bunch of classical harmonic oscillators (e.g., LC circuits or mechanical pendula) coupled in a simple manner (e.g., one dimensional chain with nearest neighbour coupling) act as a statistical-mechanics system with a well-defined temperature. That is, the modes of the system would be occupied according to a thermal distribution.
The crux of the problem is that small non-linearities result in an almost-integrable system, as in the Fermi-Pasta-Ulam-Tsingou exercise, which does not thermalize in a reasonable amount of time, therefore preventing a simple implementation.
I want to emphasize that this is a question about a closed system, and not some system coupled to a bath as that thermalizes readily.
To rephrase, is there a model of a chain of oscillators that I can realize on the top of my table and observe thermalization in? Any references or comments are highly appreciated!