By using the conserved currents associated to the diffeomorphism invariance, we study dynamical holographic systems and the relation between thermodynamical and dynamical stability of such systems. The case with fixed space-time backgrounds is discussed first, where 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 case with full back-reaction is much more complicated. With the help of conserved currents associated to the diffeomorphism invariance induced by a preferred vector field, we propose a thermodynamic form of the bulk space-time dynamics with a preferred temperature of the event horizon, where a monotonically decreasing quantity can be defined as well. In both cases, our analyses help to clarify some aspects of the far-from-equilibrium holographic physics.
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