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Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…
A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
The problem of temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a "quasi-reversible process", it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: richer feature spaces appear to favor complexity, while economic intuition has long favored parsimony. We show that this…
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory…
Let $T:X\to X $ and $S:Y \to Y$ be continuous maps defined on compact sets. Let $$\varphi_i(\mu,\nu)=\int_{X \times Y} A_i(x,y) d\mu(x) d\nu(y)\;\;{for} \;\; i=1,2,$$ where $\mu$ is $T$-invariant and $\nu$ is $S$-invariant, be pay-off…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
We argue that in the case of identical particles the most natural identification of separability, that is of absence of non-classical correlations, is via the factorization of mean values of commuting observables. It thus follows that…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…
Thermodynamical quantities of the blackbody radiation, such as free energy, entropy, total radiation energy, specific heat are calculated within the Tsallis thermostatistics where factorization method is incorparated. It is shown that basic…
A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…
We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and high energy physics. For many of these applications nonextensive properties arise from spatial fluctuations of the temperature or the…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…