  Symplectic flux measures the areas of cylinders swept in the process of a
Lagrangian isotopy. We study flux via a numerical invariant of a Lagrangian
submanifold that we define using its Fukaya algebra. The main geometric feature
of the invariant is its concavity over isotopies with linear flux.
  We derive constraints on flux, Weinstein neighbourhood embeddings and
holomorphic disk potentials for Gelfand-Cetlin fibres of Fano varieties in
terms of their polytopes. We also describe the space of fibres of almost toric
fibrations on the complex projective plane up to Hamiltonian isotopy, and
provide other applications.
