In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

let h be a finite dimensional complex hilbert space, b(h)+ be the set of all positive semi-definite operators on h and phi is a (not necessarily linear) unital map of b(h) + preserving the entropy-gibbs transformation. then there exists either a unitary or an anti-unitary operator u on h such that phi(a) = uau* for any b(h) +. thermodynamics, a branch of physics that is concerned with the study...

In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in torus, choice of moduli space allows the typical operator TFD provide degrees freedom segment and their complement. procedure, it not necessary make an analytic continuation from Rényi von Neumann calculated directly expected value operator. also propose m...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

We study the fundamental properties of the quantum f -relative entropy, where f(·) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they hold for a class of operator convex functions, and different for f(t) = − ln(t) from, the previously known conditions. The quantum f -entropy is defined in...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

It is well known that for pure states the relative entropy of entanglement equal to reduced entropy, and closest separable state explicitly as well. The same holds Renyi per recent results. We ask question a quasi-relative entanglement, which an measure defined minimum distance set state, when measured by entropy. First, we consider maximally entangled show any entanglement. Then, this also cer...