Search results
Results from the WOW.Com Content Network
The relative entropy was introduced by Solomon Kullback and Richard Leibler in Kullback & Leibler (1951) as "the mean information for discrimination between and per observation from ", [6] where one is comparing two probability measures ,, and , are the hypotheses that one is selecting from measure , (respectively).
In this form the relative entropy generalizes (up to change in sign) both the discrete entropy, where the measure m is the counting measure, and the differential entropy, where the measure m is the Lebesgue measure. If the measure m is itself a probability distribution, the relative entropy is non-negative, and zero if p = m as measures.
Informally, the quantum relative entropy is a measure of our ability to distinguish two quantum states where larger values indicate states that are more different. Being orthogonal represents the most different quantum states can be. This is reflected by non-finite quantum relative entropy for orthogonal quantum states.
The cross-entropy of the distribution relative to a distribution over a given set is defined as follows: (,) = [],where [] is the expected value operator with respect to the distribution .
Mutual information is a measure of the inherent dependence expressed in the joint distribution of and relative to the marginal distribution of and under the assumption of independence. Mutual information therefore measures dependence in the following sense: I ( X ; Y ) = 0 {\displaystyle \operatorname {I} (X;Y)=0} if and only if X ...
Generalized relative entropy (-relative entropy) is a measure of dissimilarity between two quantum states.It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity.
In 2009, Mahulikar & Herwig redefined thermodynamic negentropy as the specific entropy deficit of the dynamically ordered sub-system relative to its surroundings. [16] This definition enabled the formulation of the Negentropy Principle, which is mathematically shown to follow from the 2nd Law of Thermodynamics, during order existence.
It can also be understood to be the infinitesimal form of the relative entropy (i.e., the Kullback–Leibler divergence); specifically, it is the Hessian of the divergence. Alternately, it can be understood as the metric induced by the flat space Euclidean metric, after appropriate changes of variable.