Related papers: Lectures on Statistical Mechanics
Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of…
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main…
Lecture notes from the course given by Professor Sara A. Solla at the Les Houches summer school on "Statistical physics of Machine Learning". The notes discuss neural information processing through the lens of Statistical Physics. Contents…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
In this dissertation, we analyze equilibrium and out-of-equilibrium quantum phase transitions present in quantum spin-$\frac{1}{2}$ models, using a quantum information approach through quantum correlations and phase space formalism, and a…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
Notes for a Course on Probability and Statistics: L1: Elements of Probability; L2: Bayesian Inference; L3: Monte Carlo Methods
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
1 First Lecture: Basics 1.1 Physical Derivation of the Master Equation 1.2 Some Simple Implications 1.3 Steady State 1.4 Action to the Left 2 Second Lecture: Eigenvalues and Eigenvectors of L 2.1 A Simple Case First 2.2 The General Case 3…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…