Thermodynamics of Fractal Universe

Understand

We investigate the thermodynamical properties of the apparent horizon in a fractal universe.

• We find that one can always rewrite the Friedmann equation of the fractal universe in the form of the entropy balance relation $ \delta Q=T_h d{S_h}$, where $ \delta Q $ and $ T_{h} $ are the energy flux and Unruh temperature seen by an accelerated observer just inside the apparent horizon.
• We find that the entropy $S_h$ consists two terms, the first one which obeys the usual area law and the second part which is the entropy production term due to nonequilibrium thermodynamics of fractal universe.
• This shows that in a fractal universe, a treatment with nonequilibrium thermodynamics of spacetime may be needed.