Energies of Friedmann-Robertson-Walker universe in f(R,ϕ,X) gravity

By analyzing the energy in the sphere shell near the apparent horizon (AH), we calculate the total energy of the FRW universe and the energy of the AH in the f(R,ϕ,X) gravity. Then, we calculate the entropy production of the FRW universe in the f(R,ϕ,X) gravity. Finally, the discussion on the energy exchange between the AH and the fluid of the universe is given and the first law of thermodynamics for the AH of the FRW universe is also suggested.