  We construct a generalized Smarr formula which could provide a thermodynamic
route to derive the covariant field equation of general theories of gravity in
dynamic spacetimes. Combining some thermodynamic variables and a new chemical
potential conjugated to the number of degree of freedom on the holographic
screen, we find a universal Cardy-Verlinde formula and give its braneworld
interpretation. We demonstrate that the associated AdS-Bekenstein bound is
tighten than the previous expression for multi-charge black holes in the gauged
supergravities. The Cardy-Verlinde formula and the AdS-Bekenstein bound are
derived from the thermodynamics of bulk trapping horizons, which strongly
suggests the underlying holographic duality between dynamical bulk spacetime
and boundary field theory.
