Holography and the generalized second law of thermodynamics in (2+1)-dimensional cosmology

TL;DR

This paper examines entropy bounds in (2+1)-dimensional cosmology, finding that the Fischler-Susskind bound conflicts with the generalized second law, while the Hubble entropy bound remains compatible.

Contribution

The study compares different entropy bounds in (2+1)-dimensional universes and demonstrates the compatibility of the Hubble entropy bound with thermodynamic laws.

Findings

Fischler-Susskind bound is not satisfied in contracting universes.

Fischler-Susskind bound conflicts with the generalized second law.

Hubble entropy bound is compatible with the generalized second law.

Abstract

The Fischler-Susskind entropy bound has been studied in (2+1)-dimensional universes with negative cosmological constant. As in all contracting universes, that bound is not satisfied. Furthermore, we found that the Fischler-Susskind bound is not compatible with a generalized second law of thermodynamics in (2+1)-dimensional cosmology, neither the classical nor the quantum version. On the other hand, the Hubble entropy bound has been constructed in (2+1)-dimensional cosmology and it is shown compatible with the generalized second law of thermodynamics.