  We consider the dynamics of the charge carriers in a tunneling-enhanced
percolation network, named as a Random Resistor cum Tunneling-bond Network
(RRTN), where we allow tunneling in the gap between two randomly thrown nearest
neighbour metallic bonds only. Our earlier studies involve the dc and the ac
nonlinear response, the percolative aspects, dielectric breakdown,
low-temperature variable range hopping (VRH) conduction, etc. in the RRTN. Here
we study the non-equilibrium dynamics of the carriers. With two far-from-
equilibrium, initial inverse power-law relaxations extending over several
decades, the dynamics has a lot of similarities with a wide variety of
naturally occuring avalance-like, run-away phenomena in driven, disordered
systems with statistically correlated randomness. In the power-law regime, the
RRTN violates the Boltzmann's (or Debye) relaxation time approximation
strongly. Beyond this regime, the response relaxes exponentially fast (acquires
one time-scale) to a steady-state, and thus the relaxation approximation
becomes exact.
