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The first and generalized second laws of thermodynamics are studied in

The rapid growth of observational measurements on expansion history reveals the expanding paradigm of the universe. This fact is based on accumulative observational evidences mainly from type Ia supernova and other renowned sources [

The other promising way to deal with the cosmic expansion is the modification of Einstein-Hilbert action where it is assumed that Einstein gravity breaks down on large scales. The

In most modified gravitational theories, the Einstein gravity is generalized by changing the geometric part whereas matter part receives no attention. Bertolami et al. [

Curvature matter coupling has also been considered by introducing a Lagrangian having arbitrary dependence on the trace of energy-momentum tensor named as

The thermodynamic behavior of accelerating universe driven by DE is one of the major concerns in cosmology. It has been shown that Einstein field equations can be obtained using the relation

Akbar and Cai [

We are interested to study the thermodynamic behavior in

The paper is organized as follows. In the next section, we formulate the field equations in

The action of more general modified theory involving maximal arbitrary curvature matter coupling is of the form [

The field equations in

We can eliminate the term

In this work, we assume the FRW metric

Now, we propose to formulate the FLT in this modified theory at the apparent horizon of FRW universe. The condition

The Bekenstein-Hawking relation [

Now, we pay attention to matter energy inside a sphere of radius

In FRW framework, the energy density meets the following equation

One can retrieve

Here, we investigate the validness of GSLT in the context of

Now, we proceed to establish the GSLT in this modified theory which requires

In this setting, we limit our discussion to hypothesis of thermal equilibrium so that energy would not flow in the system and horizon temperature is more or less equal to temperature inside the horizon. This situation would correspond to the case of late times where universe components and horizon would have interacted for long time [

To illustrate the validity of GSLT in

Evolution of GSLT for the Lagrangian

Evolution of GSLT for

In this paper, we have discussed thermodynamic properties in more general modified gravity characterized by curvature matter coupling. We have found that Friedmann equations can be cast to the fundamental form of FLT

Moreover, in modified theories with explicit matter gravity coupling, we have nondiminishing covariant divergence of the energy-momentum tensor which demonstrates the energy flow due to mutual interaction of matter and gravity. The non-equilibrium treatment can be translated due to energy flow on the apparent horizon of FRW universe. We have also examined the time evolution of total entropy including the horizon entropy and entropy inside the horizon. The proportionality relation between temperature of apparent horizon and temperature associated with matter contents inside the horizon is assumed to develop the GSLT. We have also found constraints on two specific gravitational models

The authors thank the Higher Education Commission, Islamabad, Pakistanm, for its financial support through the Indigenous Ph.D. 5000 Fellowship Program Batch-VII.

_{0}universe with anisotropic dark energy

_{0}universe with anisotropic fluid