A high entropy dopant approach has been used to prepare a new BIMEVOX ceramic system, Bi2V1-x(Mg0.25Cu0.25Ni0.25Zn0.25)xO5.5-3x/2. Structures were investigated using combination of X-ray and neutron powder diffraction, with electrical characterisation by A.C. impedance spectroscopy. γ-type phase is observed at room temperature over the compositional range 0.10 ≤ x 0.30, upper limit which beyond...

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N–point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide an lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann...

In this note, we establish the first variation formula of the adjusted log entropy functional Ya introduced by Ye in [14]. As a direct consequence, we also obtain the monotonicity of Ya along the Ricci flow. Various entropy functionals play crucial role in the singularity analysis of Ricci flow. Let (M, g(t)) be a smooth family of Riemannian metrics on a closed manifold M and suppose g(t) is a ...

In this paper the notion of robust entropy and subsequently, robust entropy rate for a family of discrete time uncertain sources is introduced. When the uncertainty is described by a relative entropy constraint between the set of uncertain source densities and a given nominal source density, the solution to this robust notion of information is presented and its connection with other notions of ...

In Part 3 of this five-part article,[1, 2] simple graphic properties of entropy are illustrated, offering a novel way to understand the principle of entropy increase. The Boltzmann entropy is introduced and shows that in thermal equilibrium, entropy can be related to the spreading of a system’s occupied microstate over accessible microstates. Finally, constant-temperature reservoirs are shown t...

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statisti...

A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of a Hilbert space into two subspaces 1 and 2 is an amount of information, which can be transmitted through 1 and 2 from a system interacting with 1 to another system interacting with 2. The transmission medium is quantum entanglement between 1 and 2. In order to support the...