Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamics in $f(R,R_{\alpha\beta}R^{\alpha\beta},\phi)$ theory of
  gravity   First and second laws of black hole thermodynamics are examined at the
apparent horizon of FRW spacetime in $f(R,R_{\alpha\beta}R^{\alpha\beta}
,\phi)$ gravity, where $R$, $R_{\alpha\beta}R^{\alpha\beta}$ and $\phi$ are the
Ricci scalar, Ricci invariant and the scalar field respectively. In this
modified theory, Friedmann equations are formulated for any spatial curvature.
These equations can be presented into the form of first law of thermodynamics
for $T_{h}d\hat{S}_{h}+ T_{h}d_{i}\hat{S}_{h}+W dV=dE$, where
$d_{i}\hat{S}_{h}$ is an extra entropy term because of the non-equilibrium
presentation of the equations and $T_{h}d\hat{S}_{h}+W dV=dE$ for the
equilibrium presentation. The generalized second law of thermodynamics (GSLT)
is expressed in an inclusive form where these results can be represented in GR
$f(R)$ and $f(R, \phi)$ gravities. Finally to check the validity of GSLT, we
take some particular models and produce constraints of the parameters.

13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph