Information theory | Coding theory | Articles containing proofs | Inequalities
In information theory, Gibbs' inequality is a statement about the information entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs' inequality, including Fano's inequality.It was first presented by J. Willard Gibbs in the 19th century. (Wikipedia).
Benjamin SCHLEIN - Derivation of invariant Gibbs measures...
Derivation of invariant Gibbs measures for nonlinear Schroedinger equations from many body quantum states We prove that Gibbs measures of nonlinear Schroedinger equations of Hartree-type arise as high-temperature limits of appropriately modified thermal states in many-body quantum mechani
From playlist Trimestre "Ondes Non linéaires" - June Conference
The Gibbs phase rule tells us how many degrees of freedom we have (things we can change) while still preserving thermodynamic equilibrium of phases present.
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Uniform Probability Distribution Examples
Overview and definition of a uniform probability distribution. Worked examples of how to find probabilities.
From playlist Probability Distributions
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
Entropy production during free expansion of an ideal gas by Subhadip Chakraborti
Abstract: According to the second law, the entropy of an isolated system increases during its evolution from one equilibrium state to another. The free expansion of a gas, on removal of a partition in a box, is an example where we expect to see such an increase of entropy. The constructi
From playlist Seminar Series
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Codina Cotar: Disorder relevance for non-convex random gradient Gibbs measures in d ≤ 2
HYBRID EVENT Recorded during the meeting " Probability/PDE Interactions: Interface Models and Particle Systems " the April 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by world
From playlist Probability and Statistics
Second Law of Thermodynamics,Entropy &Gibbs Free Energy
Here is a lecture to understand 2nd law of thermodynamics in a conceptual way. Along with 2nd law, concepts of entropy and Gibbs free energy are also explained. Check http://www.learnengineering.org/2012/12/understanding-second-law-of.html to get to know about industrial applications of se
From playlist Mechanical Engineering
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
The Sherrington-Kirkpatrick model and its diluted version II
Dmitry Panchenko Texas A&M University March 12, 2014 I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main goals in these models is to find a formula for the maximum of the process, or th
From playlist Mathematics
Thermodynamics and Chemical Dynamics 131C. Lecture 22. Midterm Exam Review.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 22. Thermodynamics and Chemical Dynamics -- Midterm Exam Review -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D. License: Cre
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution
Thermodynamics and Chemical Dynamics 131C. Lecture 14. The Gibbs Energy.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 14. Thermodynamics and Chemical Dynamics -- The Gibbs Energy -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D. License: Creati
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Variational Methods: How to Derive Inference for New Models (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
Michael Kastoryano: "Classical restrictions of MPS are Gibbsian"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "Classical restrictions of MPS are Gibbsian" Michael Kastoryano - Amazon Abstract: We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems o
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Concetration for Interacting Diffusions in the KPZ Class by Philippe Sosoe
PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T
From playlist First-Passage Percolation and Related Models 2022 Edited
Fluctuations of FPP (Lecture 4) by Philippe Sosoe
PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T
From playlist First-Passage Percolation and Related Models 2022 Edited
Masha Gordina: Stochastic analysis and geometric functional inequalities
We will survey different methods of proving functional inequalities for hypoelliptic diffusions and the corresponding heat kernels. Some of these methods rely on geometric methods such as curvature-dimension inequalities (due to Baudoin-Garofalo), and some are probabilistic such as couplin
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
Paul Andersen attempts to explain Gibbs Free Energy. He begins by using three spontaneous reactions to explain how a change in enthalpy, entropy and temperature can affect the free energy of a system. He then applies this concept to cellular respiration and photosynthesis. Intro Music A
From playlist Biology