Related papers: Entropy Jumps for Radially Symmetric Random Vector…

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…

When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…

We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the…

In this short note we formulate a infinite-horizon stochastic optimal control problem for jump-diffusions of Ito-Levy type as a LP problem in a measure space, and prove that the optimal value functions of both problems coincide. The main…

The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…

A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown…

Computation of the excess entropy from the second-order density expansion of the entropy holds strictly for infinite systems in the limit of small densities. For the reliable and efficient computation of excess entropy, it is important to…

Observing stochastic trajectories with rare transitions between states, practically undetectable on time scales accessible to experiments, makes it impossible to directly quantify the entropy production and thus infer whether and how far…

This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these…

In this paper, we generalize the log-Sobolev inequalities to R\'enyi--Sobolev inequalities by replacing the entropy with the two-parameter entropy, which is a generalized version of entropy and closely related to R\'enyi divergences. We…

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…

In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy…

For a class of McKean-Vlasov stochastic differential equations with singular interactions, which include the Coulomb/Riesz/Biot-Savart kernels as typical examples (Examples 2.1 and 2.2), we derive the well-posedness and regularity estimates…

We derive a lower bound for the Wehrl entropy in the setting of SU(1,1). For asymptotically high values of the quantum number k, this bound coincides with the analogue of the Lieb-Wehrl conjecture for SU(1,1) coherent states. The bound on…

We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…

It has long been conjectured that the entropy of quantum fields across boundaries scales as the boundary area. This conjecture has not been easy to test in spacetime dimensions greater than four because of divergences in the von Neumann…

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…

Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…

How low can the joint entropy of $n$ $d$-wise independent (for $d\ge2$) discrete random variables be, subject to given constraints on the individual distributions (say, no value may be taken by a variable with probability greater than $p$,…

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…