Bochner formulas, functional inequalities and generalized Ricci flow

As a consequence of the Bochner formula for Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized Ricci flow. Using two-form potential define twisted spacetime which determines an adapted Brownian motion frame bundle, yielding Malliavin gradient path space. We this operator, leading characterizations flow in terms type associated Ornstein-Uhlenbeck operator.