Related papers: Statistical mechanics guides the motions of cm sca…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques…
Building on recent work in statistical science, the paper presents a theory for modelling natural phenomena that unifies physical and statistical paradigms based on the underlying principle that a model must be nondimensionalizable. After…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
This paper aims to justify the use of statistical mechanics tools in situations where the system is out of equilibrium and jammed. Specifically, we derive a Boltzmann equation for a jammed granular system and show that the Boltzmann's…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…
The objective of this thesis is to advance the understanding of complex physical phenomena through the lens of statistical physics. Specifically, it addresses two fundamental questions: What types of interactions can induce buckling of…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
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…
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 issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual…
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…