The generalized second law in universes with quantum corrected entropy relations

Ninfa Radicella and Diego Pavon

We apply the generalized second law of thermodynamics to discriminate among quantum corrections to the entropy of the apparent horizon in spatially Friedmann-Robertson-Walker universes.

We consider both logarithmic corrections that arise from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, and power-law corrections that appear in dealing with the entanglement of quantum fields in and out the horizon.

Cosmological equations follow either from Jacobson’s approach, that connects gravity to thermodynamics by associating Einstein equations to Clausius relation, or Padmanabhan’s suggestion that relates gravity to microscopic degrees of freedom through the principle of equipartition of energy.

We use the corresponding modified Friedmann equations along with either Clausius relation or the principle of equipartition of the energy to set limits on the value of a characteristic parameter entering the said corrections.

Both quantum corrections have been widely investigated but, since they come from very different techniques, one should not be surprised that total agreement on these corrections is still missing. In particular, there is a lack of consensus on the value of the constant parameter that multiplies such corrections. Our work aimed to discriminate among quantum corrections by requiring, via a classical analysis, the GSL to be fulfilled throughout the evolution of the Universe. This sets constraints on the value of the parameter.