Related papers: Measures maximizing the entropy for Kan endomorphi…
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A…
Given an irreducible subshift of finite type X, a subshift Y, a factor map \pi : X \to Y, and an ergodic invariant measure \nu on Y, there can exist more than one ergodic measure on X which projects to \nu and has maximal entropy among all…
Let $\mu$ be the equilibrium measure of an endomorphism of ${\sf P}^k({\bf C})$. We show that it is its unique measure of maximal entropy. We build $\mu$ directly as the distribution of any point outside an algebraic exceptional set.
In 2010, Vershik proposed a new combinatorial invariant of metric spaces given by a class of polytopes that arise in the theory of optimal transport and are called ``Wasserstein polytopes'' or ``Kantorovich-Rubinstein polytopes'' in the…
We show that every codimension one partially hyperbolic diffeomorphism must support on $\mathbb{T}^{n}$. It is locally uniquely integrable and derived from a linear codimension one Anosov diffeomorphism. Moreover, this system is…
We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…
Kovtun, Son and Starinets proposed a bound on the viscosity of any fluid in terms of its entropy density. The bound is saturated by maximally supersymmetric theories at strong coupling, but can also easily be challenged experimentally to…
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this…
We consider $C^2$ Fr\'echet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite…
We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
These lecture notes focus on a recent result of Mike Hochman: an arbitrary standard Borel system can be embedded into a mixing Markov with equal entropy, respecting all invariant probability measures, with two exceptions: those carried by…
Expanding Thurston maps form a class of branched covering maps on the topological $2$-sphere $S^{2}$, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption initially…
Let f be a holomorphic automorphism of positive entropy on a compact Kaehler surface. We show that the equilibrium measure of f is exponentially mixing. The proof uses some recent development on the pluripotential theory. The result also…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…