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Renormalization group (RG) improved cosmologies based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic parameter values are investigated using a system of cosmological evolution equations which allows for an…
The well known Hellmann-Feynman theorem of Quantum Mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition…
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
In 1935, Pauling proposed an estimate for the number of Eulerian orientations of a graph in the context of the theoretical behaviour of water ice. The logarithm of the number of Eulerian orientations, normalised by the number of vertices,…
We extend Vedral and Plenio's theorem (theorem 3 in Phys. Rev. A 57, 1619) to a more general case, and obtain the relative entropy of entanglement for a class of mixed states, this result can also follow from Rains' theorem 9 in Phys. Rev.…
Entropy generation in a chemical reaction is analyzed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic…
This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state…
Wald's entropy formula allows one to find the entropy of black holes' event horizon within any diffeomorphism invariant theory of gravity. When applied to general relativity, the formula yields the Bekenstein-Hawking result but, for any…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least…
Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…
It was shown in a previous work that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. In this paper, we go further and derive…
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to…
A new method to determine electron correlation energy is described. This method is based on a better representation of the potential due to interacting electrons that is obtained by specifying both the average and standard deviation. The…
A general Hamiltonian approach to black hole thermodynamics is used to study entropy and conserved charges for Kerr-AdS solutions in general relativity. These thermodynamic variables are first consistently defined by choosing suitable…
This paper demonstrates that basic statistics (mean, variance) of the logarithm of the variate itself can be used in the calculation of differential entropy among random variables known to be multiples and powers of a common underlying…