Related papers: Time-restricted sensitivity and entropy
Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal,…
The time until the failure of some node of the system or until the end of some stage of the operation of the tribological system is associated with the change in entropy in the system that occurs during this time. Methods of the…
This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…
We state that for continuous interval maps the existence of a non empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke,…
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…
We perform an analysis supplementing the metrology toolbox in the time-frequency domain. While the relevant time-frequency-based metrological protocols can be borrowed from the spatial domain, where they have recently been well developed,…
We introduce local topological entropy $h_{\text{top}}(T, \mathcal{U})$ and two kinds of local measure-theoretic entropy $h_{\mu}^{(r)-}(T,\mathcal{U})$ and $h_{\mu}^{(r)+}(T,\mathcal{U})$ for random bundle transformations. We derive a…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
The relative entropy of the massive free bosonic field theory is studied on various compact Riemann surfaces as a universal quantity with physical significance, in particular, for gravitational phenomena. The exact expression for the sphere…
In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…
It is widely known that when $X$ is compact Hausdorff, and when $T: X \to X$ and $f: X \to \mathbb{R}$ are continuous, \begin{equation*} P(T,f) = \sup_{\text{$\mu$: Radon probability}} \left( h_\mu(T) + \int f\, \mathrm{d}\mu \right),…
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees, thereby extending a theorem of…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
We prove that all ($\alpha$-$\beta$)-shifts with $0\le \alpha<1$ and $\beta>2$ are saturated, that is, for any invariant measure, the topological entropy of the set of generic points coincides with the metric entropy.
We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem which…