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Entropy of universe as entanglement entropy
General Relativity and Quantum Cosmology · Submitted 15 Nov 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \bar D which is not accessible by the observer.
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The abstract, sentence by sentence
We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. We argue that an appropriate spacetime region associated with an observer from tI to t_P is the causal diamond which is the overlap of the past/future of the observer at t_P/t_I respectively. We also note that the overlap surface \partial D of the future and the past lightcones bisects the spatial section including \partial D into two regions D and \bar D where D is the region inside the causal diamond and \bar D the remaining part of the spatial section. We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \bar D which is not accessible by the observer. We test our proposal for various examples of cosmological spacetimes, including flat or open FRW universes, by showing that the entropy as the area of \partial D divided by 4G is a non-decreasing function of time t_P as dictated by the generalized second law of thermodynamics. The closed, recollapsing universe corresponds to a finite system and there is no reason to expect the validity of the generalized second law for such a finite system.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. | background 0.99 | 0.26 | 0.03 | asserted 0.98 |
| s1 | We argue that an appropriate spacetime region associated with an observer from tI to t_P is the causal diamond which is the overlap of the past/future of the observer at t_P/t_I respectively. | contribution 0.56 | 0.56 | 0.05 | asserted 0.65 |
| s2 | We also note that the overlap surface \partial D of the future and the past lightcones bisects the spatial section including \partial D into two regions D and \bar D where D is the region inside the causal diamond and \bar D the remaining part of the spatial section. | background 0.56 | 0.38 | 0.03 | asserted 1.00 |
| s3 | We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \bar D which is not accessible by the observer. | contribution 0.99 | 0.60 | 0.77 | speculative 0.58 |
| s4 | We test our proposal for various examples of cosmological spacetimes, including flat or open FRW universes, by showing that the entropy as the area of \partial D divided by 4G is a non-decreasing function of time t_P as dictated by the generalized second law of thermodynamics. | result 0.85 | 0.93 | 0.34 | asserted 1.00 |
| s5 | The closed, recollapsing universe corresponds to a finite system and there is no reason to expect the validity of the generalized second law for such a finite system. | limitation 0.73 | 0.26 | 0.05 | asserted 0.74 |
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The paper
Original abstract
We note that the observable part of universe at a certain time t_P is necessarily limited, when there is a beginning of universe. We argue that an appropriate spacetime region associated with an observer from tI to t_P is the causal diamond which is the overlap of the past/future of the observer at t_P/t_I respectively. We also note that the overlap surface \partial D of the future and the past lightcones bisects the spatial section including \partial D into two regions D and \bar D where D is the region inside the causal diamond and \bar D the remaining part of the spatial section. We propose here that the entropy of universe associated with a causal diamond is given by an entanglement entropy where one is tracing over the Hilbert space associated with the region \bar D which is not accessible by the observer. We test our proposal for various examples of cosmological spacetimes, including flat or open FRW universes, by showing that the entropy as the area of \partial D divided by 4G is a non-decreasing function of time t_P as dictated by the generalized second law of thermodynamics. The closed, recollapsing universe corresponds to a finite system and there is no reason to expect the validity of the generalized second law for such a finite system.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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Recently the entropy of the universe was introduced as an entanglement entropy [ref] .
The nucleation of false vacuum bubbles with compact geometries · Introduction · 0.91
What it cites · 6 sentences without a confident label
Compares with 2 papers
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Thus for this particular observer, the holographic entanglement entropy [ref] is S_HE= A_min4G where $A_min$ denotes the area of the minimal surface, and this agrees with ours S_D=A_∂D4G since two surfaces are identical.
Holographic Derivation of Entanglement Entropy from AdS/CFT · Discussions · 0.94
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We find numerically that t_M = 0.16 ±0.01 (H^-1) , R(t_M)=0.38 ±0.02 (cH^-1) For the comparison, the cosmological event horizon is evaluated as [ref] R_CEH(t=H^-1)= c a(H^-1)∫^∞_H^-1 dxa(x)=1.13±0.05 (cH^-1) leading to the entropy of the cosmological event horizon [ref] S_CEH(t=H^-1)= 2.6±0.3 ×10^122 while the entropy of Universe in our case is S=2.9±0.3 ×10^121
A Larger Estimate of the Entropy of the Universe · Entropy of our Universe · 0.81
Cites as support 1 paper
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Even for the time dependent case, the areal entropy seems to represent the entanglement entropy as discussed in Refs. [ref] .
Three dimensional Janus and time-dependent black holes · Our proposal · 0.99
Cites as background 1 paper
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In the usual discussion of the entropy of universe [ref] - [ref] , the precise specification of the system
A Larger Estimate of the Entropy of the Universe · Our proposal · 1.00
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