Related papers: On Pinsker factors for Rokhlin entropy

Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…

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…

In this article we study $r$-neutralized local entropy and derive some entropy formulas. For an ergodic hyperbolic measure of a smooth system, we show that the $r$-neutralized local entropy equals the Brin-Katok local entropy plus $r$ times…

For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the…

In this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape of mass, the measure theoretic entropy, and the entropy at infinity of the…

We prove existence of minimizers for the sharp Poincar\'e-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are not necessarily bounded, thus the relevant embeddings may…

Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less…

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy.…

We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…

We consider spin systems in the $d$-dimensional lattice $Z^d$ satisfying the so-called strong spatial mixing condition. We show that the relative entropy functional of the corresponding Gibbs measure satisfies a family of inequalities which…

In this paper we investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system. We justify this singular limit rigorously in the framework of smooth solutions and obtain the non-isentropic…

We consider relaxation of an isolated system to the equilibrium using detailed balance condition and Onsager's fluctuation approximation. There is a small deviation from the equilibrium in two parameters. For this system, explicit…

We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…

We study topological mixing properties and the maximal equicontinuous factor of rank-one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank-one subshift is finite. We also determine all the…

The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in $f(R)$ gravity, which is an important theory could explain the accelerated…

We prove an optimal upper bound for the density of electrons of an infinite Bohr atom (no electron-electron interactions) described by the relativistic operators of Chandrasekhar and Dirac. We also consider densities in each angular…

In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials…

In this contribution we prove that the entropy of an N-body isolated system can not decrease and the entropy production should be non-negative provided the system possesses an equilibrium state. We define the entropy as a functional of the…

We construct a piecewise onto 3-to-1 dynamical system on the positive quadrant of the unit circle, such that for rational points (which correspond to normalized Primitive Pythagorean Triples), the associated ternary expansion is finite, and…

We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling…