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Mathematical physics. II, Classical statistical mechanics, lecture notes / Matteo Petrera.
- Format:
- Book
- Author/Creator:
- Petrera, Matteo, author.
- Language:
- English
- Subjects (All):
- Statistical mechanics--Textbooks.
- Statistical mechanics.
- Mathematical physics--Textbooks.
- Mathematical physics.
- Physical Description:
- 1 online resource (176 pages)
- Edition:
- 1st ed.
- Place of Publication:
- Berlin : Logos Verlag, [2014]
- Summary:
- Long description: These Lecture Notes provide an introduction to classical statistical mechanics. The first part presents classical results, mainly due to L. Boltzmann and J.W. Gibbs, about equilibrium statistical mechanics of continuous systems. Among the topics covered are: kinetic theory of gases, ergodic problem, Gibbsian formalism, derivation of thermodynamics, phase transitions and thermodynamic limit. The second part is devoted to an introduction to the study of classical spin systems with special emphasis on the Ising model. The material is presented in a way that is at once intuitive, systematic and mathematically rigorous. The theoretical part is supplemented with concrete examples and exercises.
- Contents:
- Intro
- Motivations and Background
- Introduction
- A few words about thermodynamics
- A few words about ergodic dynamical systems
- Measure spaces and measurable functions
- Probability spaces, random variables and entropy
- Ergodic dynamical systems
- Exercises
- Introduction to Kinetic Theory of Gases
- The Boltzmann kinetic theory of gases
- Derivation of the Boltzmann transport equation
- Equilibrium solutions of the Boltzmann transport equation
- Thermodynamics of a free ideal gas
- Derivation of thermodynamic properties
- Entropy and convergence to thermodynamic equilibrium
- The Kac ring model
- Gibbsian Formalism for Continuous Systems at Equilibrium
- Definition of Gibbs ensemble
- The ergodic hypothesis
- The problem of existence of integrals of motion
- Microcanonical ensemble
- Fluctuations and the Maxwell distribution
- Canonical ensemble
- Grand canonical ensemble
- Existence of the thermodynamic limit
- Van Hove interactions
- The virial expansion
- The problem of phase transitions
- Introduction to Ising Models
- Definition of Ising models
- Gibbsian formalism for Ising models
- Thermodynamics and thermodynamic limit
- One-dimensional Ising model
- Partition function
- Thermodynamics
- Two-dimensional Ising model
- Some algebraic tools: spinor analysis
- Algebraic structure of the transfer matrix
- The case H=0. Diagonalization of the transfer matrix
- The case H=0. Partition function in the thermodynamic limit
- The case H=0. Thermodynamics
- Exercises.
- Notes:
- PublicationDate: 20140915
- Description based on print version record.
- ISBN:
- 3-8325-8740-3
- 9783832587406
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