A quantity conserved to leading order when a parameter varies slowly compared with the natural motion period. The action variable of a regular periodic Hamiltonian orbit is a standard example, as explained by adiabatic invariance of the action.
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An adiabatic invariant is a quantity that remains constant when changes are made to a system very slowly, or adiabatically, compared to the timescales of the system's dynamics. The concept is often discussed in the context of classical mechanics, quantum mechanics, and thermodynamics. ### In Classical Mechanics In classical mechanics, one of the most well-known adiabatic invariants is the action variable, which is defined in the context of a periodic motion.