What's the Entropy of Gravity?

          @misc{ pirsa_PIRSA:11070059,
            doi = {10.48660/11070059},
            url = {https://pirsa.org/11070059},
            author = {Vidotto, Francesca},
            keywords = {},
            language = {en},
            title = {What{\textquoteright}s the Entropy of Gravity?},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {jul},
            note = {PIRSA:11070059 see, \url{https://pirsa.org}}
          }
          

Abstract

I present a proposal, originally motivated by a result in graph theory: the entropy function of a density matrix naturally associated to a simple undirected graph, is maximized, among all graphs with a fixed number of links and nodes, by regular graphs.I recover this result starting from the Hamiltonian operator of a non-relativistic quantum particle interacting with the loop-quantized gravitational field and setting elementary area and volume eigenvalues to a fixed value. This operator provides a spectral characterization of the physical geometry, and can be interpreted as a state describing the spectral information about the geometry available when geometry is measured by its physical interactionwith matter. It is then tempting to interpret the associated entropy function as a genuine physical entropy: I discuss the difficulties of this interpretation and I present a possible viable definition of quantum-gravitational entropy.