Related papers: Universal entropy invariants
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
We study entropies caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy and unstable topological entropy, and establish a variational principle for partially hyperbolic diffeomorphsims, which states…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
The $f$-invariant is a notion of entropy for probability-measure-preserving actions of free groups. We show it is invariant under bounded orbit-equivalence.
Free entropy is the analogue of entropy in free probability theory. The paper is a survey of free entropy, its applications to von Neumann algebras, connections to random matrix theory and a discussion of open problems.
We introduce the notion of intrinsic semilattice entropy $\widetilde h$ in the category $\mathcal L_{qm}$ of generalized quasimetric semilattices and contractive homomorphisms. By using appropriate categories $\mathfrak X$ and functors…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these invariants is obtained from the definition of L^2 homology…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
A multi-parametric version of the nonadditive entropy $S_{q}$ is introduced. This new entropic form, denoted by $S_{a,b,r}$, possesses many interesting statistical properties, and it reduces to the entropy $S_q$ for $b=0$, $a=r:=1-q$ (hence…
We compute the polynomial entropy of the induced maps on hyperspace for a homeomorphism $f$ of an interval or a circle with finitely many non-wandering points.
In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…
We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.
We find an expression for the generalized gravitational entropy of Hawking in terms of Noether charge. As an example, the entropy of the Taub-Bolt spacetime is calculated.
The expression for entropy sometimes appears mysterious - as it often is asserted without justification. This short manuscript contains a discussion of the underlying assumptions behind entropy as well as simple derivation of this…