Holographic Dark Energy Interacting with Two Fluids and Validity of
  Generalized Second Law of Thermodynamics
  We have considered a cosmological model of holographic dark energy
interacting with dark matter and another unknown component of dark energy of
the universe. We have assumed two interaction terms $Q$ and $Q'$ in order to
include the scenario in which the mutual interaction between the two principal
components (i.e., holographic dark energy and dark matter) of the universe
leads to some loss in other forms of cosmic constituents. Our model is valid
for any sign of $Q$ and $Q'$. If $Q<Q'$, then part of the dark energy density
decays into dark matter and the rest in the other unknown energy density
component. But if $Q>Q'$, then dark matter energy receives from dark energy and
from the unknown component of dark energy. Observation suggests that dark
energy decays into dark matter. Here we have presented a general prescription
of a cosmological model of dark energy which imposes mutual interaction between
holographic dark energy, dark matter and another fluid. We have obtained the
equation of state for the holographic dark energy density which is interacting
with dark matter and other unknown component of dark energy. Using first law of
thermodynamics, we have obtained the entropies for holographic dark energy,
dark matter and other component of dark energy, when holographic dark energy
interacting with two fluids (i.e., dark matter and other component of dark
energy). Also we have found the entropy at the horizon when the radius ($L$) of
the event horizon measured on the sphere of the horizon. We have investigated
the GSL of thermodynamics at the present time for the universe enveloped by
this horizon. Finally, it has been obtained validity of GSL which implies some
bounds on deceleration parameter $q$.
