Investigating the little rip and other future singularities of the universe, and validity of the second law of thermodynamics in F(R) theory

The future singularities are possible in a universe that is described by F (R) theory. In previous studies the occurrence of the singularities in F (R) theory have been considered by using a special function for the Hubble parameter and calculating the F (R) function for each of the singularities. Using the specified Hubble parameter causes some difficulties in the study of the second law of thermodynamics. In this paper by using the scale factor، the behavior of F (R) function near each type of the singularities is considered. We can check the validity of the second law of thermodynamics near the singularities. At first we study the Little Rip and then the other types of singularities are considered. The results show that the second law of thermodynamics is satisfied near the singularity type (I) with some special conditions and is violated with some other conditions. it is satisfied near the Little Rip، type (II)، (III) and (IV) singularities.