Thermodynamics of Chaplygin Gas Interacting with Cold Dark Matter

The main goal of the present work is to investigate the validity of the second law of gravitational thermodynamics in an expanding Gödel-type universe filled with generalized Chaplygin gas interacting with cold dark matter. By assuming the Universe as a thermodynamical system bounded by the apparent horizon, and calculating separately the entropy variation for generalized Chaplygin gas, cold dark matter and for the horizon itself, we obtained an expression for the time derivative of the total entropy. We conclude that the 2nd law of gravitational thermodynamics is conditionally valid in the cosmological scenario where the generalized Chaplygin gas interacts with cold dark matter.