### Abstract

Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic 'worth' of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.

Original language | English (US) |
---|---|

Pages (from-to) | 1877-1889 |

Number of pages | 13 |

Journal | Foundations of Physics |

Volume | 32 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- Black holes
- Cosmological constant
- De Sitter space
- Entropy
- Horizons
- Thermodynamics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Foundations of Physics*,

*32*(12), 1877-1889. https://doi.org/10.1023/A:1022318700787

**How far can the generalized second law be generalized?** / Davies, Paul; Davis, Tamara M.

Research output: Contribution to journal › Article

*Foundations of Physics*, vol. 32, no. 12, pp. 1877-1889. https://doi.org/10.1023/A:1022318700787

}

TY - JOUR

T1 - How far can the generalized second law be generalized?

AU - Davies, Paul

AU - Davis, Tamara M.

PY - 2002/12

Y1 - 2002/12

N2 - Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic 'worth' of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.

AB - Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic 'worth' of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.

KW - Black holes

KW - Cosmological constant

KW - De Sitter space

KW - Entropy

KW - Horizons

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=0037001956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037001956&partnerID=8YFLogxK

U2 - 10.1023/A:1022318700787

DO - 10.1023/A:1022318700787

M3 - Article

VL - 32

SP - 1877

EP - 1889

JO - Foundations of Physics

JF - Foundations of Physics

SN - 0015-9018

IS - 12

ER -