Related papers: Ergodicity: a historical perspective. Equilibrium …
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…
The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of…
The aim of this survey is to present some aspects of multifractal analysis around the recently developed subject of multiple ergodic averages. Related topics include dimensions of measures, oriented walks, Riesz products etc.
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…
In this paper we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.
In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
In this work, we introduce the concept of term ergodicity for action semigroups and construct semigroups on two dimensional manifolds which are $C^{1+\alpha}$-robustly term ergodic. Moreover, we illustrate the term ergodicity by some…
We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
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…
A classical fact in ergodic theory is that ergodicity is equivalent to almost everywhere divergence of ergodic sums of all nonnegative integrable functions which are not identically zero. We show two methods, one in the measure preserving…
We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging…