Closest separable state when measured by a quasi-relative entropy

Humans’ Closest Relative

A note on inequalities for Tsallis relative operator entropy

‎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...

Robust State Space Filtering with an Incremental Relative Entropy Tolerance

This paper considers robust filtering for a nominal Gaussian state-space model, when an incremental relative entropy tolerance is applied to each dynamical model component. The problem is formulated as a dynamic minimax game which is shown to admit a saddle point. The structure of the saddle point is characterized by applying and extending results presented earlier in [1] for static least-squar...

Relativistic Equilibrium Distribution by Relative Entropy Maximization

The equilibrium state of a relativistic gas has been calculated based on the maximum entropy principle. Though the relativistic equilibrium state was long believed to be the Jüttner distribution, a number of papers have been published in recent years proposing alternative equilibrium states. However, some of these papers do not pay enough attention to the covariance of distribution functions, r...

Bounding Relative Entropy by the Relative Entropy of Local Specifications in Product Spaces

The above inequality implies a logarithmic Sobolev inequality for q. We get an explicit lower bound for the logarithmic Sobolev constant of q under the assumptions that: (i) the local specifications of q satisfy logarithmic Sobolev inequalities with constants ρi, and (ii) they also satisfy some condition expressing that the mixed partial derivatives of the Hamiltonian of q are not too large rel...