In (2+1)-dimensional cosmology with a negative cosmological constant, the Fischler-Susskind entropy bound is incompatible with the generalized second law in contracting phases, while the Hubble entropy bound can be reconciled when quantum corrections are added.
The Generalized Second Law of Thermodynamics in Cosmology
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A classical and quantum mechanical generalized second law of thermodynamics in cosmology implies constraints on the effective equation of state of the universe in the form of energy conditions, obeyed by many known cosmological solutions, and is compatible with entropy bounds which forbid certain cosmological singularities. In string cosmology the second law provides new information about the existence of non-singular solutions, and the nature of the graceful exit transition from dilaton-driven inflation.
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Testing the Generalized Second Law in $(2+1)$-Dimensional Cosmology: Holographic Entropy Bounds and Observational Constraints
In (2+1)-dimensional cosmology with a negative cosmological constant, the Fischler-Susskind entropy bound is incompatible with the generalized second law in contracting phases, while the Hubble entropy bound can be reconciled when quantum corrections are added.