Related papers: Comments on "On q-non-extensive statistics with no…
Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…
In a recent paper, Wang. et al. (2009) claim that Tsallis' nonadditivity of q-nonextensive statistical mechanics (Gell-Mann and Tsallis 2004, Tsallis 2009) is mathematically inconsistent and hence one should carefully review Tsallis' ideas…
We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current,…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…
To discuss the existence and uniqueness of proper scoring rules one needs to extend the associated entropy functions as sublinear functions to the conic hull of the prediction set. In some natural function spaces, such as the Lebesgue…
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…
G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables…
In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or R\'enyi statistics for nonextensive systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or entropy should be…
I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst"…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies $S_{BG} \equiv -k \sum_{i=1}^W p_i \ln p_i $ and $S_{q}\equiv k (1-\sum_{i=1}^Wp_i^{q})/(q-1) (q\in{\mathbb R} ; S_1=S_{BG})$. Through…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…