Related papers: On Pinsker factors for Rokhlin entropy

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…

In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on…

We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics…

Let $G$ be a discrete countable infinite group that does not have Kazhdan's property ~(T) and let $\kappa$ be a generating probability measure on $G$. Then for each $t>0$, there is a type $III_1$ ergodic free nonsingular $G$-action whose…

Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to…

This paper proposes a new thermodynamic hypothesis that states that a nonlinear natural system that is not isolated and involves positive feedbacks tends to minimize its resistance to the flow process through it that is imposed by its…

Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…

In this paper, we investigate several types of low complexity of finite partitions, including precompactness, zero maximal pattern entropy, bounded mean complexity and mean equicontinuity. We first show that a collection of finite…

For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion…

The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic…

In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a compact metric space has a maximizing measure.…

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of $N$ coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time…

We show that a synchronized coded system $X$ is intrinsically ergodic of full support if and only if $ h(Y)$, the topological entropy of $Y$, is less than $h(X) $ whenever $Y$ is a proper subsystem of $ X $. We also show that like systems…

In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a…

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…

In a prior paper, the author generalized the classical factor theorem of Sinai to actions of arbitrary countably infinite groups. In the present paper, we use this theorem and the techniques of its proof in order to study connections…

Uncertainty is an important feature of dynamic systems, and entropy has been widely used to measure this attribute. In this Letter, we prove that state aggregation and decomposition can decrease and increase the entropy, respectively, of…

The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A…

We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…