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Entropy and Quantum Gravity
Open AccessArticle

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
Entropy 2015, 17(12), 8341-8345; https://doi.org/10.3390/e17127883
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)
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
MDPI and ACS Style

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

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