Fisher-like Metrics Associated with ϕ-Deformed (Naudts) Entropies
نویسندگان
چکیده
The paper defines and studies new semi-Riemannian generalized Fisher metrics Fisher-like metrics, associated with entropies divergences. Examples of seven such families are provided, based on exponential PDFs. particular case when the basic entropy is a ϕ-deformed one, in sense Naudts, investigated detail, emphasis variation emergent scalar curvatures. Moreover, highlights impact these geometries determined by addition some group logarithms.
منابع مشابه
deBruijn identities: from Shannon, Kullback–Leibler and Fisher to generalized φ -entropies, φ -divergences and φ -Fisher informations
In this paper we propose a generalization of the usual deBruijn identity that links the Shannon differential entropy (or the Kullback–Leibler divergence) and the Fisher information (or the Fisher divergence) of the output of a Gaussian channel. The generalization makes use of φ -entropies on the one hand, and of φ -divergences (of the Csizàr class) on the other hand, as generalizations of the S...
متن کاملContinuity of κ-deformed entropies and relative entropies
A large class of entropy functions and corresponding relative entropies is considered. Inequalities are derived, proving continuity with respect to specific distance functions. As an application it is shown that these entropies satisfy Lesche’s continuity condition. The entropies of Tsallis’ nonextensive thermostatistics are taken as examples.
متن کاملInformation, Deformed -Wehrl Entropies and Semiclassical Delocalization
Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associated Wehrl entropies, suitably κ−...
متن کاملEntropies, Volumes, and Einstein Metrics
We give an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov–Hitchin–Thorpe inequality proved in [18], and Sambusetti’s obstruction [28]. We also prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms.
متن کاملOn C3-Like Finsler Metrics
In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10224311