Related papers: Entropies of commuting transformations on Hilbert …

We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in the previous paper. We prove that every free ergodic action with finite Rokhlin entropy admits…

Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…

We prove that the (necessarily existing) pseudo-physical or SRB-like measures of C1 expanding dynamical systems on a compact Riemannian manifold satisfy Pesin entropy formula. We include examples of C1 (non C1 plus Holder) expanding maps on…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

We argue that entropy production in hydrodynamics can be understood via a superspace inflow mechanism. Our arguments are based on a recently developed formalism for constructing effective actions for Schwinger-Keldysh observables in quantum…

We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can be used to characterise Gibbs measures for expanding maps.…

This work contributes to the programme of studying effective versions of "almost everywhere" theorems in analysis and ergodic theory via algorithmic randomness. We determine the level of randomness needed for a point in a Cantor space $…

We consider a one-dimensional persisent random walk viewed as a deterministic process with a form of time reversal symmetry. Particle reservoirs placed at both ends of the system induce a density current which drives the system out of…

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion…

We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of every finite legal word exist for almost every element of the…

We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…

We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky space

In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…

We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

The study of entanglement in gauge theories is expected to provide insights into many fundamental phenomena, including confinement. However, calculations of quantities related to entanglement in gauge theories are limited by ambiguities…

We calculate the one-loop corrections to the free energy and to the entropy for fields with arbitrary spins in the space $S^1\otimes H^N$. For conformally invariant fields by means of a conformal transformation of the metric the results are…

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of…

Let $X$ be a finite set and $\Omega=\{1,...,d\}^{\mathbb{N}}$ be the Bernoulli space. Denote by $\sigma$ the shift map acting on $\Omega$. For a fixed probability $\mu$ on $X$ with supp($\mu$)$=X$, define $\Pi(\mu,\sigma)$ as the set of all…