Related papers: A Field Guide to Recent Work on the Foundations of…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
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…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in those processes renders extremely…
The booklet contain an overview on selected recent developments in nonequilibrium statistical mechanics and chaos theory: SRB distributions, chaotic hypothesis, fluctuation theorem, proposals for tests and applications to granular…
We introduce the special issue on the Statistical Mechanics of Climate published on the Journal of Statistical Physics by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great…
Machine learning is a rapidly growing field with the potential to revolutionize many areas of science, including physics. This review provides a brief overview of machine learning in physics, covering the main concepts of supervised,…
1. Connection between integration and differentiation/ Gauss theorem. Coordinate-free definitions: gradient, divergence, curl. Stokes theorem. 2. Elements of continuum mechanics/ Continuity equation. Stress tensor. Euler equation.…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for…
Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
As the title says we want to answer the question; how and why does statistical mechanics work? As we know from the most used prescription of Gibbs we calculate the phase space averages of dynamical quantities and we find that these phase…
In a recent paper by two of the authors, the concepts of upwards and downwards $\epsilon$-movability were introduced, mainly as a technical tool for studying dynamical percolation of interacting particle systems. In this paper, we further…
We introduce a fundamental theory for the kinetics of systems of classical particles. The theory represents a unification of kinetic theory, Brownian motion and field theory. It is self-consistent and is the dynamic generalization of the…