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Entropy 2015, 17(12), 8341-8345; doi:10.3390/e17127883

Gravitational Entropy and the Second Law of Thermodynamics

1
Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
2
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Academic Editors: Kevin H. Knuth and Remo Garattini
Received: 8 October 2015 / Accepted: 15 December 2015 / Published: 21 December 2015
(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)
View Full-Text   |   Download PDF [214 KB, uploaded 22 December 2015]

Abstract

The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to O(3,1) → O(3) × R , where O(3) is the rotational symmetry of the Friedmann–Lemaître–Robertson–Walker spacetime. The Weyl curvature tensor Cμνρσ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value 〈0|ψμ|0〉 ≠ 0 for a vector field ψμ acts as an order parameter and at the critical temperature Tc a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered O(3) symmetry phase the entropy is vanishingly small and for T < Tc as the universe expands the anti-restored O(3,1) Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time. View Full-Text
Keywords: gravitation; cosmology; entropy gravitation; cosmology; entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Moffat, J.W. Gravitational Entropy and the Second Law of Thermodynamics. Entropy 2015, 17, 8341-8345.

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