Related papers: Orbital free entropy, revisited

We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed…

The concept of entropy forms the backbone of the principles of thermodynamics. R.C. Tolman initiated the correlation between gravity and thermodynamics. The development of black hole thermodynamics and the generalized second law of…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

This is a review of my work published in the papers [1-4]. It offers a more detailed discussion of the results than what was given in the published papers and it links my results to some conclusions recently made by other people. It also…

The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's…

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…

A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi…

We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.

We prove that if two free p.m.p. $\mathbb{Z}$-actions are Shannon orbit equivalent then they have the same entropy. The argument also applies more generally to yield the same conclusion for free p.m.p. actions of finitely generated…

We establish several Schur-convexity type results under fixed variance for weighted sums of independent gamma random variables and obtain nonasymptotic bounds on their R\'enyi entropies. In particular, this pertains to the recent results by…

In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…

In this paper we advance the entropy theory of discrete nonautonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological…

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of…

We consider the generalization of the Araki-Uhlmann formula for relative entropy to Petz-R\'enyi relative entropy. We compute this entropy for a free scalar field in the Minkowski wedge between the vacuum and a coherent state, as well as…

Every word in a free group $F$ induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of…

We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition,…

Recently Hollands, Wald and Zhang proposed a new formula for the entropy of a dynamical black hole. We lift this construction to the dynamical cosmological event horizon of an asymptotically de Sitter spacetime. By introducing a nontrivial…