Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamics of apparent horizon and modified Friedman equations   Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent
horizon of a FRW universe, and assuming that the associated entropy with
apparent horizon has a quantum corrected relation, $S=\frac{A}{4G}-\alpha \ln
\frac{A}{4G}+\beta \frac{4G}{A}$, we derive modified Friedmann equations
describing the dynamics of the universe with any spatial curvature. We also
examine the time evolution of the total entropy including the quantum corrected
entropy associated with the apparent horizon together with the matter field
entropy inside the apparent horizon. Our study shows that, with the local
equilibrium assumption, the generalized second law of thermodynamics is
fulfilled in a region enclosed by the apparent horizon.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph