By revisiting the Kirchhoff’s Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from the graph. We use properties of the quantum relative entropy to prove tight bounds for the number of spanning trees in terms of basic parameters like degrees...

Black holes whose near–horizon geometries are locally, but not necessarily globally, AdS3 (three–dimensional anti-de Sitter space) are considered. Using the fact that quantum gravity on AdS3 is a conformal field theory, we microscopically compute the black hole entropy from the asymptotic growth of states. Precise numerical agreement with the Bekenstein-Hawking area formula for the entropy is f...

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...

The entropy of a hierarchical network topology in an ensemble of sparse random networks, with "hidden variables" associated with its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble. We obtain a general formula for this entropy, which has a clear interpretation in some simple limiting cases. The results provide keys with which to solve the general pro...

An algebraic Z-action of entropy rank one is one for which each element has finite entropy. Using the structure theory of these actions due to Einsiedler and Lind, this paper investigates dynamical zeta functions for elements of the action. An explicit periodic point formula is obtained leading to a uniform parameterization of the zeta functions that arise in expansive components of an expansiv...

Asymptotic symmetry of the Euclidean 3D gravity with torsion is described by two independent Virasoro algebras with different central charges. Elements of this boundary conformal structure are combined with Cardy’s formula to calculate the black hole entropy.

The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d − 2 obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of exam...

The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d − 2 obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of exam...

Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected quantum defect theory. This interesting when AdS bulk contains a brane (or string). We introduce for reflected entropy, which mixed state generalization of entanglement entropy measure. Based on decomposition procedure an with brane, we demonstrate equivalence between and island in AdS$_3$/BCFT$_2$. also comp...

In this article we give the detailed proof of the entropy formula for SRB-measures of coupled hyperbolic map lattices. We show that the topological pressure for the potential function of the SRB-measure is zero.