Thermodynamical aspects of modified holographic dark energy model

TL;DR

This paper explores the thermodynamics of a modified holographic dark energy model, analyzing entropy corrections and the validity of thermodynamic laws in relation to extra dimensions and the DGP model.

Contribution

It provides a systematic derivation of entropy corrections in the model and examines conditions under which thermodynamic laws hold or are violated.

Findings

Entropy correction depends on the number of extra dimensions.

The generalized second law can be violated depending on model parameters.

For more than one extra dimension, the second law always holds.

Abstract

We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it's found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale $r_c$ of the $5$-dimensional DGP model.