Braunstein–Ghosh–Severini entropy

In network theory, the Braunstein–Ghosh–Severini entropy[1][2] (BGS entropy) of a network is the von Neumann entropy of a density matrix given by a normalized Laplacian matrix of the network. This definition of entropy does not have a clear thermodynamical interpretation. The BGS entropy has been used in the context of quantum gravity.[3]

Notes and references

Braunstein, Samuel L.; Ghosh, Sibasish; Severini, Simone (2006). "The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States". Annals of Combinatorics. Springer Science and Business Media LLC. 10 (3): 291–317. arXiv:quant-ph/0406165. doi:10.1007/s00026-006-0289-3. ISSN 0218-0006. S2CID 14522309.
Anand, Kartik; Bianconi, Ginestra (13 October 2009). "Entropy measures for networks: Toward an information theory of complex topologies". Physical Review E. American Physical Society (APS). 80 (4): 045102(R). arXiv:0907.1514. Bibcode:2009PhRvE..80d5102A. doi:10.1103/physreve.80.045102. ISSN 1539-3755. PMID 19905379. S2CID 27419558.
Rovelli, Carlo; Vidotto, Francesca (24 February 2010). "Single particle in quantum gravity and Braunstein-Ghosh-Severini entropy of a spin network". Physical Review D. 81 (4): 044038. arXiv:0905.2983. Bibcode:2010PhRvD..81d4038R. doi:10.1103/physrevd.81.044038. ISSN 1550-7998. S2CID 119287145.

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[1] Braunstein, Samuel L.; Ghosh, Sibasish; Severini, Simone (2006). "The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States". Annals of Combinatorics. Springer Science and Business Media LLC. 10 (3): 291–317. arXiv:quant-ph/0406165. doi:10.1007/s00026-006-0289-3. ISSN 0218-0006. S2CID 14522309.

[2] Anand, Kartik; Bianconi, Ginestra (13 October 2009). "Entropy measures for networks: Toward an information theory of complex topologies". Physical Review E. American Physical Society (APS). 80 (4): 045102(R). arXiv:0907.1514. Bibcode:2009PhRvE..80d5102A. doi:10.1103/physreve.80.045102. ISSN 1539-3755. PMID 19905379. S2CID 27419558.

[3] Rovelli, Carlo; Vidotto, Francesca (24 February 2010). "Single particle in quantum gravity and Braunstein-Ghosh-Severini entropy of a spin network". Physical Review D. 81 (4): 044038. arXiv:0905.2983. Bibcode:2010PhRvD..81d4038R. doi:10.1103/physrevd.81.044038. ISSN 1550-7998. S2CID 119287145.