Related papers: Generalized Statistics Variational Perturbation Ap…
A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…
For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…
We discuss the generalized von Neumann (Tsallis) entropy and the generalized Fisher information (GFI) in nonextensive quantum systems, by using the interpolation approximation (IA) which has been shown to yield good results for the quantal…
A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis' entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is…
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…
The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is…
Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has garnered considerable popularity in recent years, for example, in the analysis of multivariate abundance data in ecology.…
We revisit the derivation of a formula for the $q$-generalised multinomial coefficient rooted in the $q$-deformed algebra, a foundational framework in the study of nonextensive statistics. Previous approximate expressions in the literature…
Using the methodology of conditional-probability density functional theory, and several mild assumptions, we calculate the temperature-dependence of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). This…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
By use of the gauge-invariant variables proposed by Kodama and Ishibashi, we obtain the most general perturbation equations in the $(m+n)$-dimensional spacetime with a warped product metric. These equations do not depend on the spectral…
The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…
Distribution shifts between sites can seriously degrade model performance since models are prone to exploiting unstable correlations. Thus, many methods try to find features that are stable across sites and discard unstable features.…
A variational principle for the rate distortion (RD) theory with Bregman divergences is formulated within the ambit of the generalized (nonextensive) statistics of Tsallis. The Tsallis-Bregman RD lower bound is established. Alternate…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…