  We study the generalized K\"ahler-Ricci flow with initial data of symplectic
type, and show that this condition is preserved. In the case of a Fano
background with toric symmetry, we establish global existence of the normalized
flow. We derive an extension of Perelman's entropy functional to this setting,
which yields convergence of nonsingular solutions at infinity. Furthermore, we
derive an extension of Mabuchi's $K$-energy to this setting, which yields weak
convergence of the flow.
