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- Publisher Website: 10.1088/1361-6382/aafec7
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Article: Volume entropy
Title | Volume entropy |
---|---|
Authors | |
Keywords | loop quantum gravity spin networks spacetime thermodynamics spacetime entropy volume operator |
Issue Date | 2019 |
Citation | Classical and Quantum Gravity, 2019, v. 36, n. 5, article no. 055012 How to Cite? |
Abstract | © 2019 IOP Publishing Ltd Printed in the UK. Building on a technical result by Brunnemann and Rideout on the spectrum of the volume operator in loop quantum gravity, we show that the dimension of the space of the quadrivalent diffeomorphism invariant states with no zero-volume nodes describing a region with total volume smaller than V has finite dimension, bounded by V log V. This implies that a notion of 'volume entropy' may be introduced on this state space, interpreted as the von Neumann entropy associated to the measurement of volume. However, it also becomes apparent that including the states with vanishing volume eigenvalues this entropy becomes divergent. We briefly discuss possible implications of this conundrum and difficulties arising for extending this analysis to higher valent nodes. |
Persistent Identifier | http://hdl.handle.net/10722/285834 |
ISSN | 2023 Impact Factor: 3.6 2023 SCImago Journal Rankings: 1.232 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Astuti, Valerio | - |
dc.contributor.author | Christodoulou, Marios | - |
dc.contributor.author | Rovelli, Carlo | - |
dc.date.accessioned | 2020-08-18T04:56:46Z | - |
dc.date.available | 2020-08-18T04:56:46Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Classical and Quantum Gravity, 2019, v. 36, n. 5, article no. 055012 | - |
dc.identifier.issn | 0264-9381 | - |
dc.identifier.uri | http://hdl.handle.net/10722/285834 | - |
dc.description.abstract | © 2019 IOP Publishing Ltd Printed in the UK. Building on a technical result by Brunnemann and Rideout on the spectrum of the volume operator in loop quantum gravity, we show that the dimension of the space of the quadrivalent diffeomorphism invariant states with no zero-volume nodes describing a region with total volume smaller than V has finite dimension, bounded by V log V. This implies that a notion of 'volume entropy' may be introduced on this state space, interpreted as the von Neumann entropy associated to the measurement of volume. However, it also becomes apparent that including the states with vanishing volume eigenvalues this entropy becomes divergent. We briefly discuss possible implications of this conundrum and difficulties arising for extending this analysis to higher valent nodes. | - |
dc.language | eng | - |
dc.relation.ispartof | Classical and Quantum Gravity | - |
dc.subject | loop quantum gravity | - |
dc.subject | spin networks | - |
dc.subject | spacetime thermodynamics | - |
dc.subject | spacetime entropy | - |
dc.subject | volume operator | - |
dc.title | Volume entropy | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1088/1361-6382/aafec7 | - |
dc.identifier.scopus | eid_2-s2.0-85062626017 | - |
dc.identifier.volume | 36 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | article no. 055012 | - |
dc.identifier.epage | article no. 055012 | - |
dc.identifier.eissn | 1361-6382 | - |
dc.identifier.isi | WOS:000458633700003 | - |
dc.identifier.issnl | 0264-9381 | - |