Related papers: Ergodicity: a historical perspective. Equilibrium …
A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics
Our goal in this short note is to briefly and succinctly describe some basic concepts and properties of Ergodic Optimization for readers unfamiliar with the subject. We avoid technical issues in order to provide a global overview of this…
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns {\it nonextensive}…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
Translation of Ludwig Boltzmann's paper "\"Uber die Eigenschaften monozyklischer und anderer damit verwandter Systeme" Crelles Journal 98. S. 68-94. 1884 u. 1885 from German into English. In this foundational paper Boltzmann introduced two…
Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
In this talk we present some studies in the approach to equilibrium of the classical lambda phi^4 theory on the lattice, giving particular emphasis to its pedagogical usefulness in the context of classical statistical field theory (such as…
We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.
This is a survey on Sarnak's Conjecture
This survey is a 2022 update of the 2008 version, with recent developments and new references.
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
The paradoxes of thermodynamics and statistical physics are unavoidable in the study of physical paradoxes because of their importance at the time they came to be as well as the frequency of their appearance in historical studies of…
We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main…
Boltzmann's ergodic hypothesis furnishes a possible explanation for the emergence of statistical mechanics in the framework of classical physics. In quantum mechanics, the Eigenstate Thermalization Hypothesis (ETH) is instead generally…
It is well known that ergodic theory can be used to formally prove a weak form of relaxation to equilibrium for finite, mixing, Hamiltonian systems. In this Letter we extend this proof to any dynamics that preserves a mixing equilibrium…
We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropies