Please pardon the non-accidental facetiousness (because you and I may have a surprisingly common set of interests),-- But: you can first extend the boundary of

Please pardon the non-accidental facetiousness (because you and I may have a surprisingly common set of interests),-- But: you can first extend the boundary of what is meant by "physical quantity" to the Non-Archimedean https://en.wikipedia.org/wiki/Ultrametric_space#Applications https://en.wikipedia.org/wiki/Ultrametric_space#Applications and then think about going even further https://en.wikipedia.org/wiki/Self-averaging#Non_self-averaging_systems https://en.wikipedia.org/wiki/Self-averaging#Non_self-averag...