Thermodynamics of dark energy interacting with dark matter and radiation

TL;DR

The paper addresses whether the generalized second law of thermodynamics holds in a cosmology where dark energy interacts with dark matter and radiation. It develops a general three-fluid FRW model with interaction terms $Q$ and $Q'$ and recasts it into an effective uncoupled description, then computes the total entropy change on the apparent horizon with $T_h=1/(2\\pi \\tilde r_A)$ and $S_h=8\\pi^2 \\tilde r_A^2$. The main result is an explicit, horizon-based entropy rate $\\dot S_{tot}=4\\pi^2 \\tilde r_A^6 H [ (1+w_{DE})\\rho_{DE}+(1+w_M)\\rho_M+(1+w_\\chi)\\rho_\\chi]^2 \\ge 0$, showing the generalized second law holds regardless of coupling details, EOS values, or background geometry under FRW cosmology; using the future event horizon would yield only conditional validity. The work also discusses a critical phantom EOS where the total entropy rate vanishes and highlights the implications for phantom thermodynamics and horizon choice in cosmological thermodynamics.

Abstract

We investigate the validity of the generalized second law of thermodynamics, in the cosmological scenario where dark energy interacts with both dark matter and radiation. Calculating separately the entropy variation for each fluid component and for the apparent horizon itself, we show that the generalized second law is always and generally valid, independently of the specific interaction form, of the fluids equation-of-state parameters and of the background geometry.