In the background of the homogeneous and isotropic FLRW model, the thermodynamics of the interacting DE fluid is investigated in the present work. By studying the thermodynamical parameters, namely the heat capacities and the compressibilities, both thermal and mechanical stability are discussed and the restrictions on the equation of state parameter of the dark fluid are analyzed.

The present work deals with homogeneous and isotropic FLRW model of the Universe having a system of non-interacting diffusive cosmic fluids with barotropic equation of state (constant or variable equation of state parameter). Due to diffusive nature of the cosmic fluids, the divergence of the energy momentum tensor is chosen to be proportional to the diffusive current. The thermodynamic stability analysis of individual fluids is done and the stability conditions are expressed as restrictions on the equation of state parameter.

The work deals with the thermodynamical aspects of the cosmic substratum which is dissipative in nature. For homogeneous and isotropic model of the Universe this dissipative phenomenon is effective bulk viscous pressure in nature and is related to the particle creation mechanism. Finally, the stability criteria for the thermal equilibrium has been analyzed and are presented in tabular form restricting the particle creation parameter or the variation of the equation of state parameter with the volume.

In the present work, we have made an attempt to investigate the dark energy possibility from the thermodynamical point of view. For this purpose, we have studied thermodynamic stability of three popular dark energy models in the framework of an expanding, homogeneous, isotropic and spatially flat FRW Universe filled with dark energy and cold dark matter. The models considered in this work are Chevallier-Polarski-Linder (CPL) model, Generalized Chaplygin Gas (GCG) model and Modified Chaplygin Gas (MCG) model. By considering the cosmic components (dark energy and cold dark matter) as perfect fluid, we have examined the constraints imposed on the total equation of state parameter (wT ) of the dark fluid by thermodynamics and found that the phantom nature (wT < −1) is not thermodynamically stable. Our investigation indicates that the dark fluid models (CPL, GCG and MCG) are thermodynamically stable under some restrictions of the parameters of each model. PACS numbers: 98.80.Hw, 98.80.Jk, 98.80.Cq, 05.70.Ce.

A study of the universal thermodynamics has been done for the inhomogeneous Friedmann–Lemaitre–Robertson–Walker type (FLRW-type) space-time model. Validity of the generalized second law of thermodynamics has been examined across an arbitrary horizon and integrability condition for the generalized Gibbs equation has been determined. Also, the conditions for thermodynamical equilibrium have been presented in a tabular form. Finally, using unified first law, the corrected Bekenstein entropy has been evaluated for both apparent and event horizons.