K6132020 Thermodynamics and Statistical Mechanics

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Engineering

Lecture Code K6132020 Subject Classification Specialized Education

Subject Name 熱・統計力学

Subject Name
（Katakana）ネツ・トウケイリキガク

Subject Name in
English Thermodynamics and Statistical Mechanics

Instructor NISHIDA MUNEHIRO

Instructor
(Katakana) ニシダ　ムネヒロ

Campus Higashi-Hiroshima Semester/Term 3rd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Fri5-8：ENG 102

Lesson Style Lecture Lesson Style
(More Details) 　

Hybrid  lectures

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 12 : Electronics

Eligible Students 3rd year students of Cluster 2 (Electrical, Electronic and Systems Engineering)

Keywords Microcanonical ensemble, Canonical ensemble, Grand canonical ensemble, Partition function, Entropy, Free energy, Fermi distribution function

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Many advanced problems in the fields of electrical, computer and systems engineering relate to the electronics based of the electronic properties of solids. Therefore, the understanding ot the electronic properties is one of the important elements to solve the problems in these fields.
In this course, students will learn the fundamentals of Statistical Mechanics and Thermodynamics necessary to understand the electoronic properties of solids, and learn the basics of how to deal with various problems relating to electrons.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Program of Electronic Devices and Systems
（Abilities and Skills）
・Concepts, knowledge and methods which are the basis for studies related to electronic engineering.

Class Objectives
/Class Outline The objective of this class is to provide the basic knowledge of Statistical Mechanics and Thermodynamics which is necessary to understand electronic properties of solids.
Especially, students should be able to understand the following topics.
1. Concepts of microcanonical ensemble and entropy
2. Concept of canonical ensemble
3. Concept of grand canonical ensemble
4. Meaning and usage of partition function
5. Meaning and usage of Fermi distribution function
6. Concepts of free energies

Class Schedule lesson1: Basic concepts in Statistical Mechanics
  principle of equal a priori probabilities, Stirling's formula
  [short test] Stirling's formula
lesson2: Entropy 1
  microcanonical ensemble, definition of entropy, absolute temperature
  [short test] temperature at equilibrium
lesson3: Entropy 2
  entropy of harmonic oscillators, adiabatic theorem, pressure of a gass
  [short test] entropy
lesson4: Canonical ensemble and free energy 1
  canonical ensemble, partition function, fluctuation of energy, specific heat
  [short test] partition function and energy
lesson5: Canonical ensemble and free energy 2
  Helmholtz free energy, principle of minimum free energy
  [short test] partition function of harmonic oscillators
lesson6: Canonical ensemble and free energy 3
  Gibbs free energy, state quantity, Legendre transformation
  [short test] free energy
lesson7: Grand canonical ensemble and chemical potential 1
  grand canonical ensemble, chemical potential, grand partition function
  [short test] grand partition function
lesson8: Grand canonical ensemble and chemical potential 2
  average and fluctuation of particle number, physical meaning of chemical potential
  [short test] chemical potential
lesson9: Summary of the first half, Mid-term examination
lesson10: Lows of Thermodynamics
  grand partition function and state quantities, thermodynamic functions, thermodynamic relations
  [short test] thermodynamic relations
lesson11: Classical statistical mechanics and the law of equipartition of energy
  approximation of classical statistical mechanics, ideal gass, law of equipartition of energy
  [short test] approximation of classical statistical mechanics
lesson12: Fermi-Dirac statistics and free electron gass 1
  quantum statistics, derivation of Fermi distribution function
  [short test] free electron gass
lesson13: Fermi-Dirac statistics and free electron gass 2
  free electron gass, Fermi momentum, Fermi energy
  [short test] Fermi momentum, Fermi energy
lesson14: Applications of Statistical Mechanics 1
  statistical mechanics of electrons in semiconductors
  [short test] carrier density
lesson15: Applications of Statistical Mechanics 2
  lattice vibrations of solids, Debye temperature, specific heat
  [short test] lattice vibrations

Text/Reference
Books,etc. Reference：
長岡洋介「統計力学」（岩波書店）

PC or AV used in
Class,etc. 　

(More Details) Handouts. Please bring your PC to take online quizzes.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review It is necessary to review each class enough to solve the short tests given in every class by yourself.
It will help your understanding to read the following pages of the reference book before each lesson.

長岡洋介「統計力学」（岩波書店）
Lesson 1: p.1-17
Lesson 2: p.18-29
Lesson 3: p.50-60
Lesson 4: p.69-78
Lesson 5: p.78-86
Lesson 6: p.86-90
Lesson 7: p.167-170, 190-193
Lesson 8: p.170-173, 193-194
Lesson 9: mid-term examination
Lesson 10: p.90-96
Lesson 11: p.99-109, 115-119
Lesson 12: p.197-201, 206-209
Lesson 13: p.209-225
Lesson 14: p.226
Lesson 15: p.154-164

Requirements Prerequisites: taking the class "Introduction to Physical Electronics" and having a basic knowledge of quantum mechanics.

Grading Method Your final grade will be based on the following: short tests (40%), mid-term online examination (30%), term-end online examination (30%).
If the condition of the COVID-19 infection is improved, a face-to-face exams may be conducted.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message Office hour: 16:20-17:20 on every Friday

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Engineering
Lecture Code	K6132020	Subject Classification	Specialized Education
Subject Name	熱・統計力学
Subject Name （Katakana）	ネツ・トウケイリキガク
Subject Name in English	Thermodynamics and Statistical Mechanics
Instructor	NISHIDA MUNEHIRO
Instructor (Katakana)	ニシダ　ムネヒロ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Fri5-8：ENG 102
Lesson Style	Lecture	Lesson Style (More Details)
Hybrid lectures
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	12 : Electronics
Eligible Students	3rd year students of Cluster 2 (Electrical, Electronic and Systems Engineering)
Keywords	Microcanonical ensemble, Canonical ensemble, Grand canonical ensemble, Partition function, Entropy, Free energy, Fermi distribution function
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Many advanced problems in the fields of electrical, computer and systems engineering relate to the electronics based of the electronic properties of solids. Therefore, the understanding ot the electronic properties is one of the important elements to solve the problems in these fields. In this course, students will learn the fundamentals of Statistical Mechanics and Thermodynamics necessary to understand the electoronic properties of solids, and learn the basics of how to deal with various problems relating to electrons.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Program of Electronic Devices and Systems （Abilities and Skills）・Concepts, knowledge and methods which are the basis for studies related to electronic engineering.
Class Objectives /Class Outline	The objective of this class is to provide the basic knowledge of Statistical Mechanics and Thermodynamics which is necessary to understand electronic properties of solids. Especially, students should be able to understand the following topics. 1. Concepts of microcanonical ensemble and entropy 2. Concept of canonical ensemble 3. Concept of grand canonical ensemble 4. Meaning and usage of partition function 5. Meaning and usage of Fermi distribution function 6. Concepts of free energies
Class Schedule	lesson1: Basic concepts in Statistical Mechanics principle of equal a priori probabilities, Stirling's formula [short test] Stirling's formula lesson2: Entropy 1 microcanonical ensemble, definition of entropy, absolute temperature [short test] temperature at equilibrium lesson3: Entropy 2 entropy of harmonic oscillators, adiabatic theorem, pressure of a gass [short test] entropy lesson4: Canonical ensemble and free energy 1 canonical ensemble, partition function, fluctuation of energy, specific heat [short test] partition function and energy lesson5: Canonical ensemble and free energy 2 Helmholtz free energy, principle of minimum free energy [short test] partition function of harmonic oscillators lesson6: Canonical ensemble and free energy 3 Gibbs free energy, state quantity, Legendre transformation [short test] free energy lesson7: Grand canonical ensemble and chemical potential 1 grand canonical ensemble, chemical potential, grand partition function [short test] grand partition function lesson8: Grand canonical ensemble and chemical potential 2 average and fluctuation of particle number, physical meaning of chemical potential [short test] chemical potential lesson9: Summary of the first half, Mid-term examination lesson10: Lows of Thermodynamics grand partition function and state quantities, thermodynamic functions, thermodynamic relations [short test] thermodynamic relations lesson11: Classical statistical mechanics and the law of equipartition of energy approximation of classical statistical mechanics, ideal gass, law of equipartition of energy [short test] approximation of classical statistical mechanics lesson12: Fermi-Dirac statistics and free electron gass 1 quantum statistics, derivation of Fermi distribution function [short test] free electron gass lesson13: Fermi-Dirac statistics and free electron gass 2 free electron gass, Fermi momentum, Fermi energy [short test] Fermi momentum, Fermi energy lesson14: Applications of Statistical Mechanics 1 statistical mechanics of electrons in semiconductors [short test] carrier density lesson15: Applications of Statistical Mechanics 2 lattice vibrations of solids, Debye temperature, specific heat [short test] lattice vibrations
Text/Reference Books,etc.	Reference：長岡洋介「統計力学」（岩波書店）
PC or AV used in Class,etc.
(More Details)	Handouts. Please bring your PC to take online quizzes.
Learning techniques to be incorporated
Suggestions on Preparation and Review	It is necessary to review each class enough to solve the short tests given in every class by yourself. It will help your understanding to read the following pages of the reference book before each lesson. 長岡洋介「統計力学」（岩波書店） Lesson 1: p.1-17 Lesson 2: p.18-29 Lesson 3: p.50-60 Lesson 4: p.69-78 Lesson 5: p.78-86 Lesson 6: p.86-90 Lesson 7: p.167-170, 190-193 Lesson 8: p.170-173, 193-194 Lesson 9: mid-term examination Lesson 10: p.90-96 Lesson 11: p.99-109, 115-119 Lesson 12: p.197-201, 206-209 Lesson 13: p.209-225 Lesson 14: p.226 Lesson 15: p.154-164
Requirements	Prerequisites: taking the class "Introduction to Physical Electronics" and having a basic knowledge of quantum mechanics.
Grading Method	Your final grade will be based on the following: short tests (40%), mid-term online examination (30%), term-end online examination (30%). If the condition of the COVID-19 infection is improved, a face-to-face exams may be conducted.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	Office hour: 16:20-17:20 on every Friday
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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