Related papers: Quasi-additivity of Tsallis entropies and correlat…
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…
It is presented a generalization of the von Neumann mutual information in the context of Tsallis' nonextensive statistics. As an example, entanglement between two (two-level) quantum subsystems is discussed. Important changes occur in the…
We derive the multiplicative duality "q<->1/q" and other typical mathematical structures as the special cases of the (mu,nu,q)-relation behind Tsallis statistics by means of the (mu,nu)-multinomial coefficient. Recently the additive duality…
Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We show that the restricted sharability and distribution of multi-qubit entanglement can be characterized by Tsallis-$q$ entropy. We first provide a class of bipartite entanglement measures named Tsallis-$q$ entanglement, and provide its…
We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in \mathbb{R}^N$ are…
We study the thermodynamical properties of the quantum kicked rotator, coarsened by an external fluctuation with a weak intensity D, by means of the Tsallis entropy with a changing entropic index q. The genuine entropic index, corresponding…
We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…
In this research paper, it is proved that an approximation to Gibbs-Shannon entropy measure naturally leads to Tsallis entropy for the real parameter q =2 . Several interesting measures based on the input as well as output of a discrete…
The equivalence between Tsallis Thermodynamics and Hill Nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the…
It is known that when a system interacts with its environment, the entanglement contained in the system is redistributed since parts of the system entangle with the environment. On the other hand, the entanglement of a system with its…
For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of $q$-canonical ensembles, also known as Tsallis statistics. These conditions are invariance requirements over the…
Increasing the number $N$ of elements of a system typically makes the entropy to increase. The question arises on {\it what particular entropic form} we have in mind and {\it how it increases} with $N$. Thermodynamically speaking it makes…
Quantum entanglement and quantum entropy are crucial concepts in the study of multipartite quantum systems. In this work we show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and…
Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive…
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
The connection between Tsallis entropy for a multifractal distribution and Jackson's $q$-derivative is established. Based on this derivation and definition of a homogeneous function, a $q$-analogue of Shannon's entropy is discussed.…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…