Related papers: Telescopic Relative Entropy--II Triangle inequalit…
We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore…
The quantum relative entropy $S(\rho||\sigma)$ is a widely used dissimilarity measure between quantum states, but it has the peculiarity of being asymmetric in its arguments. We quantify the amount of asymmetry by providing a sharp upper…
We introduce "Replicated Entanglement Entropy (REE)" as the entanglement entropy of a subspace in a replicated theory. We calculate this quantity by replicating the original theory in two steps along the same entangling region and taking…
A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
Quantum relative entropy $D(\rho\|\sigma)\defeq\Tr \rho (\log \rho- \log \sigma)$ plays an important role in quantum information and related fields. However, there are many quantum analogues of relative entropy. In this paper, we…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
We establish the theories of Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the internal-space and investigate possible internal-space symmetries among primary constraint densities in the theories. First of all, we…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR),…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
Penrose conjectured a connection between entropy and Weyl curvature of the Universe. This is plausible, as the almost homogeneous and isotropic Universe at the onset of structure formation has negligible Weyl curvature, which then grows…
Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The…
In an earlier study, we showed that Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to non-extensive systems, can be used as a possible risk measure in constructing risk optimal…
The logarithm of the number of Eulerian orientations, normalised by the number of vertices, is known as the residual entropy in studies of ice-type models on graphs. The spanning tree entropy depends similarly on the number of spanning…
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $\rho$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space…
When the difference between changes in energy and entropy at a given temperature is correlated with the ratio between the same changes in energy and entropy at zero average free energy of an ensemble of similar but distinct molecule-sized…