  In this work, we have considered that the flat FRW universe is filled with
the mixture of dark matter and the new holographic dark energy. If there is an
interaction, we have investigated the natures of deceleration parameter,
statefinder and $Om$ diagnostics. We have examined the validity of the first
and generalized second laws of thermodynamics under these interactions on the
event as well as apparent horizon. It has been observed that the first law is
violated on the event horizon. However, the generalized second law is valid
throughout the evolution of the universe enveloped by the apparent horizon.
When the event horizon is considered as the enveloping horizon, the generalized
second law is found to break down excepting at late stage of the universe.
