  A possible source of black hole entropy could be the entanglement of quantum
fields in and out the horizon. The entanglement entropy of the ground state
obeys the area law. However, a correction term proportional to a fractional
power of area results when the field is in a superposition of ground and
excited states. Inspired by the power-law corrections to entropy and adopting
the viewpoint that gravity emerges as an entropic force, we derive modified
Newton's law of gravitation as well as the corrections to Friedmann equations.
In a different approach, we obtained power-law corrected Friedmann equation by
starting from the first law of thermodynamics at apparent horizon of a FRW
universe, and assuming that the associated entropy with apparent horizon has a
power-law corrected relation. Our study shows a consistency between the
obtained results of these two approaches. We also examine the time evolution of
the total entropy including the power-law corrected entropy associated with the
apparent horizon together with the matter field entropy inside the apparent
horizon and show that the generalized second law of thermodynamics is fulfilled
in a region enclosed by the apparent horizon.
