  For divisors over smooth projective varieties, we show that the volume can be
characterized by the duality between pseudo-effective cone of divisors and
movable cone of curves. Inspired by this result, we give and study a natural
intersection-theoretic volume functional for 1-cycles over compact K\"ahler
manifolds. In particular, for numerical equivalence classes of curves over
projective varieties, it is closely related to the mobility functional.
