  In this paper, we study thermodynamics of the cluster of galaxies under the
effect of dynamical dark energy. We evaluate the configurational integral for
interacting system of galaxies in an expanding universe by including the
effects produced by the varying $\Lambda$. The gravitational partition function
is obtained using this configuration integral. We obtain thermodynamics
quantities in canonical ensemble which depend on time and investigate the
second law of thermodynamics. We also calculate the distribution function in
grand canonical ensemble. The time evolution of the clustering parameter of
galaxies is investigated for the time dependent (dynamical) dark energy. We
conclude that the second law of thermodynamics is valid for the total system of
cluster of galaxies and dynamical dark energy. We calculate correlation
function and show that our model is very close to Peebles's power law, in
agreement with the N-body simulation. It is observed that thermodynamics
quantities depend on the modified clustering parameter for this system of
galaxies.
