We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes’ inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the nonnegative matrices in the framework of matrix ana...

Abstract For over two decades entropy theory has been applied to groundwater modeling with particular regard to (1) groundwater head, (2) parameter estimation, and (3) contaminant transport. Entropy theory is formulated in two domains: real domain and frequency domain. In the real domain, the theory comprises (a) Shannon entropy or another form, (2) principle of maximum entropy, (3) relative en...

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving co...

Abstract. We give a new characterization of relative entropy, also known as the Kullback–Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a finite set equipped with a probability distribution, while a morphism is a measure-preserving function f : X → Y together with a stochastic right in...

In this paper the principle of minimum relative entropy (PMRE) is proposed as a fundamental principle and idea that can be used in the field of AGI. It is shown to have a very strong mathematical foundation, that it is even more fundamental then Bayes rule or MaxEnt alone and that it can be related to neuroscience. Hierarchical structures, hierarchies in timescales and learning and generating s...

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum and another state, both reduced to a local region. We propose that, with the adequate interpretation, the positivity of the relative entropy in this case cons...

In this expository article, we study optimization problems specified via linear and relative entropy inequalities. Such relative entropy programs (REPs) are convex optimization problems as the relative entropy function is jointly convex with respect to both its arguments. Prominent families of convex programs such as geometric programs (GPs), second-order cone programs, and entropymaximization ...

Authorship attribution is the task of deciding who wrote a particular document. Several attribution approaches have been proposed in recent research, but none of these approaches is particularly satisfactory; some of them are ad hoc and most have defects in terms of scalability, effectiveness, and efficiency. In this paper, we propose a principled approach motivated from information theory to i...

It was proved that quantum relative entropy D(k) is attained by a certain sequence of measurements which is independent of. This formula is thought to be important for the quantum asymptotic detection and the quantum asymptotic estimation. To know the quantum asymptotic estimation, see [13]. The constructions of these applications are, however, left for future study. Acknowledgments I wish to t...

Pattern recognition is a collection of computer techniques to classify various observations into different clusters of similar attributes in either supervised or unsupervised manner. Application of fuzzy logic to unsupervised classification or clustering methods has resulted in many wildly used techniques such as fuzzy c-means (FCM) method. However, when the observations are too noisy, the perf...