Before revision:  We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints . This class of dynamics covers major payoff-based (non-imitative) evolutionary dynamics. The key is expected net gains (payoff improvements) from strategy revisions after paying switching costs. Static stability implies that the aggregate net gain diminishes over time under economic reasonable dynamics and thus can be used as a Lyapunov function.
After revision:  We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints behind distortions from exact optimization. This idea guides us to track the remaining expected maximal payoff gain from switches, after deducting the costs and to be maximized subject to the constraints, as a disequilibrium index, namely, a Lyapunov function.