相关论文: Variants of the Entropy Power Inequality

We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…

We show that odd order R\'enyi entropies $S^{(2q+1)}$ of a system of interacting scalar fields can be calculated as the free energy of $2q+1$ replicas of the system with additional quadratic inter-replica couplings in the subsystem at the…

It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds with the differential entropy replaced by…

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.

This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing…

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…

Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…

A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential…

Entropy functionals are computed for non-stationary distributions of particles of Lorentz gas and hard disks. The distributions consisting of beams of particles are found to have the largest amount of entropy and entropy increase. The…

A method is presented for computing the R\'enyi entropy of a perturbed massless vacuum on the ball via a comparison with lattice field theory. If the perturbed state is Gaussian with smoothly varying correlation functions and the…

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…

An expression for the effective action of a conformal scalar on odd spheres allows a relatively simple computation of the expansion coefficients of the R\'enyi entropy for any odd dimension, d. Explicit values are listed for d=3,5 and 7.…

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with…

The R\'enyi entropies of quasiparticle excitations in the many-body gapped systems show a remarkable universal picture which can be understood partially by combination of a semiclassical argument with the quantum effect of…

Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new…

Pinsker-type inequalities are considered for the weighted total variation distance between probability measures in terms of the R\'enyi divergence powers. They are applied in derivation of transport-entropy inequalities under moment-type…

The analogues of Arimoto's definition of conditional R\'enyi entropy and R\'enyi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to…

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…