A variational expression for the relative entropy
نویسندگان
چکیده
منابع مشابه
A Variational Expression for the Relative Entropy
We prove that for the relative entropy of faithful normal states φ and ω on the von Neumann algebra M the formula S(φ,ω) = sup{ω(Λ)-logφ(/): h = h*eM] holds. In general von Neumann algebras the relative entropy was defined and investigated by Araki [1, 3]. After Lieb had proved the joint convexity of the relative entropy in the type / case [10] several proofs appeared in the literature and they...
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In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, {em Math. Inequal. Appl.} {18} (2015), no. 2, 401--406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...
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We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of “almost Gibbsian measures” (almost sure continuity of conditional probabilities). For quasilocal measures, we obtain a full variational principle. For the joint measures of the random field Ising model, we show ...
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in this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by zou [operator inequalities associated with tsallis relative operator entropy, {em math. inequal. appl.} {18} (2015), no. 2, 401--406]. meanwhile, we also show some new lower and upper bounds for relative operator entropy and tsallis relative o...
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The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1988
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf01225040