  By using the conserved currents in the bulk space-time, we study dynamical
holographic systems and the relation between thermodynamical and dynamical
stability of such systems. In particular, in the probe limit a generalized free
energy is defined with the property of monotonic decreasing in dynamic
processes. It is then shown that the (absolute) thermodynamical stability
implies the dynamical stability, while the linear dynamical stability implies
the thermodynamical (meta-)stability. The holographic superfluid is taken as an
example to illustrate our general formalism, where the dynamic evolution of the
system in contact with a particle source is clarified by theoretical
investigation and numerical verification. The case going beyond the probe limit
is also discussed.
