Is symplectic form $dp_i \wedge dq_i$ in Hamiltonian mechanics a physical quantity? It feels to me to be something different than say energy, momentum or mass. Like just certain structure.
The real reason why I'm asking lies not in mechanics, but in GENERIC. There apart of Poisson bracket the second bracket is added. This bracket is responsible for the irreversible evolution and depends highly on a physical system in hand. While I was musing about it I wondered whether I can attribute these two brackets as physical quantities and if no, how shall I at least call them as opposed to physical quantities?