Related papers: Ergodicity, ensembles, irreversibility in Boltzman…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…
This letter raises the possibility that ergodicity concerns might have some bearing on the signal-to-noise paradox. This is explored by applying the ergodic theorem to the theory behind ensemble weather forecasting and the ensemble mean.…
The purpose of this article is to highlight the fascinating, but only very incompletely understood relation between Einstein's theory and its generalizations on the one hand, and the theory of indefinite, and in particular hyperbolic, Kac…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies,…
This paper has been withdrawn by the authors, due a crucial error.
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these…
Various diagnostics of the emergence of an arrow of time in the bulk description of a holographic theory have been proposed, including the decay of some real time correlation functions and the appearance of type III$_1$ von Neumann algebras…
A recent essay [1] reminds us of how richly Boltzmann deserves to be admiringly commemorated for the originality of his ideas on the occasion of his 150th birthday. Without any doubt, the scientific community owes Boltzmann a great debt of…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
This article is part of a series of works by the authors with the goal of completing a far-reaching program propounded by Deligne, aiming to extend the codimension one part of the Grothendieck-Riemann-Roch theorem from isomorphism classes…
Emergence is a pregnant property in various fields. It is the fact for a phenomenon to appear surprisingly and to be such that it seems at first sight that it is not possible to predict its apparition. That is the reason why it has often…
The design of deep neural networks remains somewhat of an art rather than precise science. By tentatively adopting ergodic theory considerations on top of viewing the network as the time evolution of a dynamical system, with each layer…
In this work we have carried out an approach between the nonsingular scientific cosmologies (without the initial singularity, the big bang), specially the cyclic models, and the Nietzsche's thought of the eternal recurrence. Moreover, we…
In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena…
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…