In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has many physical meanings, as discussed in . (Wikipedia).
Steffen Borgwardt: The role of partition polytopes in data analysis
The field of optimization, and polyhedral theory in particular, provides a powerful point of view on common tasks in data analysis. In this talk, we highlight the role of the so-called partition polytopes and their studies in clustering and classification. The geometric properties of parti
From playlist Workshop: Tropical geometry and the geometry of linear programming
Probability Distribution Functions and Cumulative Distribution Functions
In this video we discuss the concept of probability distributions. These commonly take one of two forms, either the probability distribution function, f(x), or the cumulative distribution function, F(x). We examine both discrete and continuous versions of both functions and illustrate th
From playlist Probability
Cumulative Distribution Functions and Probability Density Functions
This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or nor
From playlist Statistics
Partitions of a Set | Set Theory
What is a partition of a set? Partitions are very useful in many different areas of mathematics, so it's an important concept to understand. We'll define partitions of sets and give examples in today's lesson! A partition of a set is basically a way of splitting a set completely into disj
From playlist Set Theory
Probability Density Functions (3 of 7: Unknowns in the function)
More resources available at www.misterwootube.com
From playlist Random Variables
Cumulative Distribution Functions (CDFs)
Explain the relationship between a PDF and a CDF (Probability Density Function and Cumulative Distribution Function). Go through some examples at the level of Yr 12 Methods QLD
From playlist Statistics - MAM Unit 4
Discrete Math - 2.3.4 Useful Functions to Know
Ceiling function, floor function and factorial function. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Split function example. Calculus for Beginners - Dr Chris Tisdell Live Stream
Split functions follow one rule and the swtich to another rule, depending on where you are on a x-axis. I define what a split function is (also called a picewise defined function) and discuss and example. In mathematics, functions are an important tool for understanding how things depend
From playlist Calculus for Beginners
Molecular Structure & Statistical Mechanics 131B. Lecture 24. Partition Functions Pt. 2
UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 24. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 2. View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html Instruc
From playlist Chem 131B: Week 10
Chem 131B. Molecular Structure & Statistical Mechanics. Lecture 23. Partition Functions Pt. 1
UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 23. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 1. View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html Instruc
From playlist Chem 131B: Molecular Structure & Statistical Mechanics
Thermodynamics and Chemical Dynamics 131C. Lecture 04. Entropy.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 04. Thermodynamics and Chemical Dynamics -- Entropy -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D. License: Creative Common
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Geometry – Partitioning a Segment – Video Lecture Topics discussed include: directed line segments, ratios, slope, finding a point that partitions a segment to a specified ratio.
From playlist Geometry
Statistical Mechanics of Vortices by Nick Manton
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Quantum Mechanics 1.2: The Planck Distribution
Twitter: https://twitter.com/SciencePlease_ In part 1.2 of this quantum mechanics series, we look at Max Planck's quantum resolution to solve the ultraviolet catastrophe.
From playlist Quantum Mechanics
Algebraic combinatorics: applications to statistical mechanics and complexity theory - Greta Panova
Short proofs are hard to find (joint work w/ Toni Pitassi and Hao Wei) - Ian Mertz Computer Science/Discrete Mathematics Seminar II Topic: Short proofs are hard to find (joint work w/ Toni Pitassi and Hao Wei) Speaker: Ian Mertz Affiliation: University of Toronto Date: December 5, 2017 F
From playlist Mathematics
Lecture 4 | Modern Physics: Statistical Mechanics
April 20, 2009 - Leonard Susskind explains how to calculate and define pressure, explores the formulas some of applications of Helm-Holtz free energy, and discusses the importance of the partition function. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies P
From playlist Lecture Collection | Modern Physics: Statistical Mechanics
Molecular Structure & Statistical Mechanics 131B. Lecture 26. Final Exam Review
UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 26. Molecular Structure & Statistical Mechanics -- Final Exam Review. View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html Instructor: Rachel
From playlist Chem 131B: Week 10
Statistical Mechanics Lecture 4
(April 23, 2013) Leonard Susskind completes the derivation of the Boltzman distribution of states of a system. This distribution describes a system in equilibrium and with maximum entropy. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.st
From playlist Course | Statistical Mechanics
Statistical Mechanics Lecture 5
(April 29, 2013) Leonard Susskind presents the mathematical definition of pressure using the Helmholtz free energy, and then derives the famous equation of state for an ideal gas: pV = NkT. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.s
From playlist Course | Statistical Mechanics
In this video we cover some rational function fundamentals, including asymptotes and interecepts.
From playlist Polynomial Functions