The idea of statistical mechanics structured similarly to onion was discussed before (13 Sep 2024). I was watching lectures about the fitness landscape in evolution. The fitness landscape consists of adaptation peaks and also includes paths to those peaks.
In comparison, wave statistical mechanics is a set of numerous elements (call it A). Instead of finding peaks, actions should be discovered such that it turns B (a subset of A) into a wave group. The action, that is defined in wave group B, can be some functionality in a specific species. It’s also possible that B is a set of elements which contains elements of several species plus for example environmental elements, then the action in wave group B is a symmetry that includes different species and environmental elements.
Imagine m is a member of wave group B_1 (where B_1 is limited to one species) and also is a member of B_2 (where B_2 contains several species and environmental elements), then m exists in different layers. Currently, in statistical mechanics, elements of the system (molecules for example) are contained in one layer only, but in wave statistical mechanics each element can be in several layers. So the same set of elements (i.e. set A) includes different layers. Each group then corresponds with a probability, specifying how probable it is that a specific group is picked. So each mutation is linked with several probabilities because it exists in different groups.
This totally differentiates the fitness landscape from the wave layer-by-layer structure.
UPDATE 1:
This idea can also be expanded to politics. Each voter can be a member of several groups in different layers. This is linked to the idea of social distances (see 30 Aug 2024 and 22 July 2024). If there are two main parties and most people support one of them or the other then polarization is inevitable because people in one party oppose whatever the other party says. But if the political spectrum is based on a layer-by-layer structure people can oppose each other on some issues but not all issues.
To unify opposition for instance (because opposition normally consists of different approaches) this layer-by-layer structure can be very beneficial.