--- title: Statistical Mechanics description: Statistical mechanics applies probability theory to large assemblies of microscopic particles. Learners will understand how macroscopic thermodynamic properties, like temperature and entropy, emerge from the microscopic states of individual atoms and molecules. category: mathematics subcategory: mathematical-physics difficulty: beginner, intermediate, advanced url: /subject/statistical-mechanics --- # Statistical Mechanics Statistical mechanics applies probability theory to large assemblies of microscopic particles. Learners will understand how macroscopic thermodynamic properties, like temperature and entropy, emerge from the microscopic states of individual atoms and molecules. ## Available Resources 3 Books • 5 Courses • 2 Websites ## Websites ### 1. David Tong Lecture Notes Cambridge Part II lecture notes by David Tong covering the microcanonical, canonical and grand canonical ensembles, classical and quantum gases, and phase transitions. The exposition is unusually readable, with worked examples and problem sheets alongside. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.damtp.cam.ac.uk/user/tong/statphys.html **Tags:** statistical ensembles, phase transitions, quantum gases, lecture notes, Cambridge ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ## Courses ### 1. Introduction to Statistical Physics (MIT RES.8-010) **Author:** Mobolaji Williams A short introduction pitched at advanced high-school students: entropy from probability, the laws of thermodynamics, and the Boltzmann distribution for systems at finite temperature. Lecture notes, problem sets and a final exam, all with solutions, plus practice writing simple simulations of random events. **Difficulty:** Beginner | **Price:** Free **Link:** https://ocw.mit.edu/courses/res-8-010-introduction-to-statistical-physics-summer-2018/ **Tags:** statistical-physics, entropy, thermodynamics, boltzmann-distribution, probability ### 2. Information and Entropy (MIT 6.050J) **Author:** Paul Penfield, Seth Lloyd The physical limits of communication and computation: digital signals, codes and compression, noise and error correction, probability, channel capacity, reversible and quantum computation, and entropy's link to the second law of thermodynamics. Includes an open textbook, programming assignments and 11 problem sets with solutions. **Difficulty:** Beginner | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-050j-information-and-entropy-spring-2008/ **Tags:** information-theory, entropy, error-correcting-codes, data-compression, physics-of-computation ### 3. Statistical Mechanics II: Statistical Physics of Fields (MIT 8.334) **Author:** Mehran Kardar Second semester of graduate statistical mechanics: collective behavior, phase transitions, Landau-Ginzburg theory, scaling, the renormalization group and critical phenomena in classical field theories. Includes 26 lecture videos, lecture notes, problem sets and exams with solutions, preparing learners to analyze universality near critical points. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2014/ **Tags:** statistical-field-theory, phase-transitions, renormalization-group, critical-phenomena, landau-ginzburg-theory ### 4. Statistical Mechanics I: Statistical Mechanics of Particles (MIT 8.333) **Author:** Mehran Kardar A graduate treatment of thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics and identical particles. Includes 26 lecture videos, detailed lecture notes, problem sets and exams with solutions, building the tools to derive equilibrium properties of many-particle systems. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2013/ **Tags:** statistical-mechanics, statistical-ensembles, kinetic-theory, quantum-statistics, interacting-systems ### 5. Statistical Mechanics We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/physics/ecole-polytechnique-federale-de-lausanne-advanced-statistical-physics **Tags:** courses, science-research, mathematical-physics ## Books ### 1. Statistical Mechanics **Author:** R.K. Pathria A graduate textbook building statistical mechanics from ensemble theory through ideal Bose and Fermi systems, phase transitions, and fluctuations. It is the standard first-year reference for students who already have thermodynamics and quantum mechanics behind them. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0080189946?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics ### 2. Statistical Physics **Author:** L.D. Landau, E.M. Lifshitz Volume 5 of the Course of Theoretical Physics, deriving thermodynamics and statistical physics from first principles with terse, general arguments. Demanding but rewarding; it treats fluctuations, phase transitions, and Fermi and Bose gases at professional depth. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0750633727?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics ### 3. Introduction to Statistical Physics **Author:** Kerson Huang An undergraduate text by an MIT physicist that moves from thermodynamic laws and kinetic theory to Bose-Einstein condensation and broken symmetry. Shorter and gentler than his graduate volume, it suits a first serious course in the subject. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0748409424?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/statistical-mechanics