statistical physics problems and solutions pdf

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It does

" My memory for figures, otherwise tolerably accurate, always lets me down when I am counting beer glasses. "

      -- Ludwig Boltzmann.

The Maxwell-Boltzmann Distribution.

David Tong: Lectures on Statistical Physics

This is an introductory course on Statistical Mechanics and Thermodynamics given to final year undergraduates. They were last updated in May 2012. Full lecture notes come in around 190 pages. Individual chapters and problem sets can also be found below.

  • 1. Fundamentals of Statistical Mechanics:   PDF Introduction; Microcanonical Ensemble; Entropy and the Second Law; Temperature; Two-State Spin System; First Law of Thermodynamics; Canonical Ensemble; Energy Fluctuations; Chemical Potential; Grand Canonical Ensemble.
  • 2. Classical Gases:   PDF Classical Partition Functions; Ideal Gas; Equipartition; Maxwell Distribution; Diatomic Gas; Interactions; van der Waals Equation of State; Cluster Expansion; Debye-Huckel model.
  • 3. Quantum Gases:   PDF Density of States; Blackbody Radiation; Debye Model of Vibrations in a Solid; Diatomic Gas Revisted, Bose-Einstein Distribution and Bose-Einstein Condensation; Fermi-Dirac Distribution and Fermi Gas; White Dwarfs; Pauli Paramagnetism; Landau Diamagnetism.
  • 4. Classical Thermodynamics:   PDF Temperature and the Zeroth Law; The First Law; The Second Law; Carnot Cycles; Entropy; Adiabatic Surfaces; Maxwell Relations; The Third Law.
  • 5. Phase Transitions:   PDF van der Waals equation Revisited; Phase Equilibrium; Maxwell Construction; Clausius-Clapyron Equation; Critical Point; Ising Model; Mean Field Theory; Critical Exponents; Ising Chain; Low Temperature Expansion and Peierls Droplets; High Temperature Expansion; Kramers-Wannier Duality; Landau Theory; Lee-Yang Zeros; Landau-Ginzburg Theory; Fluctuations and Correlations.

Problem Sheets

  • Problem Sheet 1:   Postscript     PDF    Ensembles   
  • Problem Sheet 2:   Postscript     PDF    Classical and Quantum Gases   
  • Problem Sheet 3:   Postscript     PDF    Bosons and Fermions   
  • Problem Sheet 4:   Postscript     PDF    Thermodynamics and Phase Transitions

Statistical Physics on the Web

  • Statistical Mechanics of Particles:    Mehran Kardar's lectures from MIT.
  • Statistical Mechanics of Fields:    The second installment of Mehran Kardar's lectures.
  • Thermodynamics and Statistical Mechanics    Lecture Notes by Daniel Arovas (links directly to pdf file)
  • Statistical Physics    A three semester course from Caltech by Michael Cross

Other Resources

  • E.T. Jaynes on the Gibb's Paradox .
  • Lecture notes copyright © 2011 David Tong unless otherwise credited. Permission is granted to copy and distribute freely, so long as proper attribution is given, no alterations are made, and no monetary profit is gained. The first image is taken from Philosophy of Science Department at The second is taken from Wikipedia, credit to Dswartz4 (hat tip Jack Thorne).

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Fundamentals Of Statistical And Thermal Physics Reif Solutions Manual

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statistical physics problems and solutions pdf

Statistical Physics

An Advanced Approach with Applications

  • © 2012
  • Latest edition
  • Josef Honerkamp 0

Fakultät für Physik, Universität Freiburg, Freiburg, Germany

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  • Focuses on concepts and methods in statistics, giving detailed insight in analyzing physical data
  • Provides an thorough introduction to statistical physics with an emphasis on the analysis of statistical systems
  • Includes advanced topics, reference lists, problems with solutions and boxed inserts, making it an invaluable source for students, even after completion of the course
  • The introduction to filters, wavelets and many practical and concrete algorithms close a noticeable gap left open by other textbooks
  • Third edition offers 50 pages of new material, especially on data-analysis, Gillespie-algorithm, Kaiman filters, plus new problems with solutions
  • Covers all modern applications of statistics
  • Includes supplementary material:

Part of the book series: Graduate Texts in Physics (GTP)

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Table of contents (13 chapters)

Front matter, modeling of statistical systems, statistical physics is more than statistical mechanics.

Josef Honerkamp

Random Variables: Fundamentals of Probability Theory and Statistics

Random variables in state space: classical statistical mechanics of fluids, random fields: textures and classical statistical mechanics of spin systems, time-dependent random variables: classical stochastic processes, quantum random systems, changes of external conditions, analysis of statistical systems, estimation of parameters, signal analysis: estimation of spectra, estimators based on a probability distribution for the parameters, identification of stochastic models from observations, estimating the parameters of a hidden stochastic model, statistical tests and classification methods, back matter.

  • Data Analysis Statistical Physics
  • Hidden Stochastic Model
  • Modeling Statistical Systems
  • Signal Analysis Spectrum
  • Statistical test Method
  • Textbook Data Analysis
  • Textbook Statistical Mechanics
  • Textbook Statistical Physics

About this book

The application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well.

The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of  problems with solutions is accessible on the Web at

From the book reviews:

“The book is carefully divided into two parts. The first part deals with modeling of statistical systems. The second part is devoted to the analysis of the respective systems. … followed by a section that offers helpful hints and solutions to problems throughout the text, making it easier for students to deepen their understanding and confidence in their newfound knowledge. … topics in each chapter are carefully selected and are well presented, making it a reliable reference for ‘statistical physics.’” (Technometrics, Vol. 55 (2), May, 2013)

Authors and Affiliations

About the author, bibliographic information.

Book Title : Statistical Physics

Book Subtitle : An Advanced Approach with Applications

Authors : Josef Honerkamp

Series Title : Graduate Texts in Physics


Publisher : Springer Berlin, Heidelberg

eBook Packages : Physics and Astronomy , Physics and Astronomy (R0)

Copyright Information : Springer-Verlag Berlin Heidelberg 2012

Hardcover ISBN : 978-3-642-28683-4 Published: 22 June 2012

Softcover ISBN : 978-3-642-44385-5 Published: 18 July 2014

eBook ISBN : 978-3-642-28684-1 Published: 19 June 2012

Series ISSN : 1868-4513

Series E-ISSN : 1868-4521

Edition Number : 3

Number of Pages : XIV, 554

Topics : Complex Systems , Mathematical Methods in Physics , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences , Statistical Physics and Dynamical Systems

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Course info.

  • Prof. Mehran Kardar


As taught in.

  • Probability and Statistics
  • Theoretical Physics
  • Thermodynamics

Learning Resource Types

Statistical mechanics ii: statistical physics of fields.

The 3 in-class tests are composed entirely from a subset of the problem sets. The tests are ‘closed book,’ but students may bring a one-sided sheet of formulas.

Below are review problems from previous tests.


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  1. PDF Solutions Manual for Introduction to Statistical Physics (draft)

    Introduction to Statistical Physics 1- Obtain the probability of adding up six points if we toss three distinct dice. *** Let·s consider an easier problem, two dice, for exam-ple. In this (simpler) case, there are 6 6 = 36 con-gurations (events), but only 5 of them correspond to 6 points. Since all of

  2. (PDF) Problems & Solutions for Statistical Physics of Particles

    See Full PDFDownload PDF. Problems & Solutions for Statistical Physics of Particles Updated July 2008 by Mehran Kardar Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA fTable of Contents I. Thermodynamics II.

  3. Problem Sets

    Starter Problem Set with Solutions (PDF) Workshop Problem Set 1: Taylor Series, Probability, and Combinatorics (PDF) Workshop Problem Set 2: Mean-Field Ising Model (PDF) Workshop Problem Set 3: Simulating a Spin System (PDF)

  4. PDF Problems and Solutions in

    These exercises were submitted during my teaching of Statistical Mechanics at the University of Naples "Federico II". They occasionally refer to my textbook, L. Peliti, Statistical Mechanics in a Nutshell (Princeton: Princeton U. P., 2012). I am grateful to my colleagues and especially to my students, who helped shape the problems and their ...

  5. PDF Physics 210a : Statistical Physics Final Exam Solutions

    energy. In general, one must find the nontrivial (i.e. x 6= 0 ) solution of the simultaneous equations f(x,θ) = f0 and ∂f/∂x = 0 for the two unknowns θ and x to obtain the critical values (θc,xc) at the first order transition. (4) Provide brief but accurate answers to each of the following:

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    Yung-Kuo Lim Problems and Solutions on Thermodynamics and Statistical Mechanics.pdf. Skip to main content. We will keep fighting for all libraries - stand with us! ... Yung-Kuo Lim Problems and Solutions on Thermodynamics and Statistical Mechanics.pdf. Addeddate 2017-11-09 03:13:18

  7. PDF Statistical Physics

    Landau and Lifshitz, Statistical Physics Russian style: terse, encyclopedic, magni cent. Much of this book comes across as remarkably modern given that it was rst published in 1958. Mandl, Statistical Physics This is an easy going book with very clear explanations but doesn't go into as much detail as we will need for this course.

  8. Assignments

    Statistical Physics I. Menu. More Info Syllabus Calendar Readings, Notes & Slides Assignments Exams Assignments. LEC # PROBLEMS SOLUTIONS 3 Problem Set 1 (PDF) ... Problem Set 9 Solutions (PDF) 20 Problem Set 10 (PDF) Problem Set 10 Solutions (PDF) 22 Problem Set 11 (PDF) Problem Set 11 Solutions (PDF) Course Info

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    II. Quick introduction into probability and statistics. 4 A. Discrete Sets. 5 B. Continuous distributions. 10 C. Problems for Sec. II 17 III. Microscopic ensembles, ergodicity 17 A. Problems for Sec. III 24 IV. Entropy, temperature, laws of thermodynamics. 24 A. Statistical Entropy 24 B. Temperature 26 C. First law of thermodynamics. 27 D.

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  11. David Tong: Statistical Physics

    David Tong: Lectures on Statistical Physics. This is an introductory course on Statistical Mechanics and Thermodynamics given to final year undergraduates. They were last updated in May 2012. Full lecture notes come in around 190 pages. Individual chapters and problem sets can also be found below. PDF HTML Español.

  12. PDF Statistical Mechanics

    are \essential problems". These problems are so important to the development of the course material that you must do them to have any hope of being able to understand the course material. Essential problems are either relied upon in later text material (e.g. problem 1.2) or else cover important topics

  13. Statistical Mechanics: Problems with solutions

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  15. Fundamentals Of Statistical And Thermal Physics Reif Solutions Manual

    solutions manual of Fundamentals of statistical and thermal physics Reif which is the best book on the fields on statistical as well as thermal physics Addeddate 2016-06-25 08:21:43

  16. PDF This content has been downloaded from IOPscience. Please scroll down to

    an additional file Test Problems with Solutions. Distinguishing features of this series—in brief • condensed lecture notes (∼250 pp per semester)—much shorter than most textbooks • emphasis on simple explanations of the main notions and phenomena of physics • a focus on problem solution; extensive sets of problems with detailed model

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    Statistical Mechanics I: Exam Review 1 Solution. 8.333: Statistical Mechanics I Fall 2007 Test 1. . Review Problems. The first in-class test will take place on Wednesday 9/26/07 from 2:30 to 4:00 pm. There will be a recitation with test review on Friday 9/21/07. The test is 'closed book,' but if you wish you may bring a one-sided sheet of ...

  18. Statistical Physics: An Advanced Approach with Applications

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    Problem 4.2: Find the number of ways in which 8 persons can be assigned to 2 rooms (A and B) if each room must have at least 3 persons in it. Solution 4.2: The number of persons in the room is between 3 and 5. Let us start with the situation where room A has 3 persons. The number of ways to do that is 8 · 7 · 6.

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    Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: Thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

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    Qualifying Exam Solutions: Thermal Physics and Statistical Mechanics Alexandre V. Morozov 1 Solutions for Problem 1 a) Q= 0 for adiabatic processes, and thus the rst law of thermodynamics becomes: U+ A= 0; (1) where Ais the work done by gas, and U is its internal energy. Using A= P 2 V and U= C V Twe obtain: C V(T 2 T 1) + P 2(V 2 V 1) = 0: (2)

  22. Exams

    The 3 in-class tests are composed entirely from a subset of the problem sets. The tests are "closed book," but students may bring a one-sided sheet of formulas. All topics presented in the course will be covered in the final exam, with emphasis on the second half. The exam is closed book, but students may bring a two-sided sheet of formulas.

  23. Exams

    Exams. The 3 in-class tests are composed entirely from a subset of the problem sets. The tests are 'closed book,' but students may bring a one-sided sheet of formulas. Below are review problems from previous tests.