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This paper explores the nonequilibrium behavior of thermodynamics at the apparent horizon of isotropic and homogeneous universe model in

The discovery of current cosmic accelerated expansion has stimulated many researchers to explore the cause of this tremendous change in cosmic history. A mysterious force known as dark energy (DE) is considered as the basic ingredient responsible for this expanding phase of the universe. Dark energy has repulsive nature with negatively large pressure but its complete characteristics are still unknown. Modified gravity theories are considered as the favorable and optimistic approaches to unveil the salient features of DE. These modified theories of gravity are obtained by replacing or adding curvature invariants as well as their corresponding generic functions in the Einstein-Hilbert action.

Gauss-Bonnet (GB) invariant is a linear combination of quadratic invariants of the form

The curvature-matter coupling in modified theories has attained much attention to discuss the cosmic accelerated expansion. Harko et al. [

The significant connection between gravitation and thermodynamics is established after the remarkable discovery of black hole (BH) thermodynamics with Hawking temperature as well as BH entropy [

The generalized second law of thermodynamics (GSLT) has a significant importance in modified theories of gravity. Wu et al. [

In this paper, we investigate the first as well as second law of thermodynamics at the apparent horizon of FRW model with any spatial curvature. The paper has the following format. In Section

The action of

The covariant derivative of (

The energy-momentum tensor for perfect fluid as cosmic matter contents is given by

The line element for FRW universe model is

In this section, we study the laws of thermodynamics in the context of

The first law of thermodynamics is based on the concept that energy remains conserved in the system but can change from one form to another. To study this law, we first find the dynamical apparent horizon evaluated by the relation

Bekenstein-Hawking entropy is defined as one-fourth of apparent horizon area

The surface gravity

In this section, we discuss the GSLT in

Now we check the validity of GSLT for some reconstructed cosmological models in

The well-known cosmological de Sitter solution elegantly describes the evolution of current cosmic expansion. For this model, the Hubble parameter is constant

Figures

Validity of GSLT for the model (

Validity of GSLT for the model (

The graphical behavior of GSLT for de Sitter

Validity of GSLT for the model (

Validity of GSLT for the model (

Power-law solution has remarkable importance in modified theories of gravity to discuss the decelerated as well as accelerated cosmic evolutionary phases which are characterized by the scale factor as [

The validity of GSLT for models (

Validity of GSLT for the model (

Validity of GSLT for the model (

The validity of GSLT for the model (

Validity of GSLT for the model (

Validity of GSLT for the model (

In this paper, we have investigated the first and second laws in the nonequilibrium description of thermodynamics and also checked the validity of GSLT for reconstructed models in

We have found the general expression for the validity of GSLT in terms of horizon entropy, entropy production term, and entropy corresponding to all matter and energy contents inside the horizon. For nonequilibrium picture of thermodynamics, it is assumed that temperature associated with all matter and energy contents inside the horizon is always positive and smaller than the temperature at apparent horizon. It is found that viability condition for this law is consistent with the universal condition for its validity in modified theories of gravity [

For de Sitter reconstructed models, it is found that the validity of GSLT is true for model (

For power-law reconstructed models, the valid results are found when integration constant

We conclude that the validity condition of GSLT is true for both reconstructed de Sitter and power-law

The authors have no conflicts of interest.

The authors would like to thank the Higher Education Commission, Islamabad, Pakistan, for its financial support through the