Related papers: Ergodicity: a historical perspective. Equilibrium …
These notes are based on a course for a general audience given at the Centro de Modeliamento Matem\'atico of the University of Chile, in December 2004. We study the mean convergence of multiple ergodic averages, that is, averages of a…
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
A brief but complete historical survey of the theory of equilibrium figures from its early origins, dating back to 17th-century, until the latest 20th-century developments, with a view towards its applications, is carried out.
These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…
We show that in classical spin systems the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium…
Non-ergodicity impacts statistical inference in a diverse range of disciplines inside and outside of physics. However the concept of ergodicity is used inconsistently, and may refer to several nonequivalent notions. To help address this, we…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
We discuss the foundations of the statistical gravity theory we proposed in a recent publication [Riccardo Fantoni, Quantum Reports, {\bf 6}, 706 (2024)].
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamical formalism which leads to a multifractal spectrum. It is proved that…
It is argued that a diffusion may be ergodic even though the drift field has unbounded outward-directed parts. The discussion employs stochastic and numerical methods.
In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…
An introductory review of Classical Statistical Mechanics
Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated…
This note analyzes the physical basis of J.R. England's paper "Statistical physics of self-replication." [J. Chem. Phys. {\bf 139}, 121923(2013)]. We follow England's use of time-reversal symmetry but replace stochastic by deterministic…
Given are a first principles derivation and formulation of the probabilistic concepts that underly equilibrium quantum statistical mechanics. The transition to non-equilibrium probability is traversed briefly.
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…