An energy landscape assigns an energy to each possible state and describes its variation between neighbouring states. Its local minima and intervening energy barriers help distinguish favourable states from states that a specified dynamics can reach quickly. In a Hopfield network, the assigned energy is an objective function and need not be a conserved physical quantity.
An energy barrier is an increase in energy that must be overcome along an allowed route between states. Its value depends on which paths or single-step moves are allowed; specifying only the energies of the endpoints does not determine the barrier.

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