Statistical mechanics combines principles of statistics and mechanics to predict and explain measurable properties of macroscopic systems based on microscopic constituents. It discusses three types of statistics: classical Maxwell-Boltzmann statistics, Bose-Einstein statistics for integer spin particles like photons allowing multiple occupancy, and Fermi-Dirac statistics for half-integer spin fermions like electrons following Pauli's exclusion principle of single occupancy. The document provides examples and characteristics of each statistical approach.

1. Welcome all

2. Mathematical Physics and
Statistical Mechanics
Dr.S.Amudha
by

3. Statistical mechanics, branch of physics that combines the
principles and procedures of statistics with the laws of both
classical and quantum mechanics, particularly with respect to
the field of thermodynamics.
It aims to predict and explain the measurable properties of
macroscopic systems on the basis of the properties and behavior
of the microscopic constituents of those systems.
Definition for statistical
mechanics

4. Types of statistical
mechanics
Classical or Maxwell
Boltzmann statistics
Quantum statistics
Bose Einstein
statistics
Fermi dirac
statistics

5. Classical or Maxwell Boltzmann statistics
explains temperature, pressure, energy.
But it does not explain the concept such as
Black body radiation
Photo-electric effect
Specific heat capacity at low temperatures

6. Classical or Maxwell Boltzmann [MB]
Statistics Characteristics
 Identical
 Distinguishable
 Any spin
 Example: Molecules of gas

7. In this case the particles are distinguishable so
let’s label them A and B. Let’s call the 2 single
particle states 1 and 2. For Maxwell–Boltzmann
statistics any number of particles can be in any
state. So let’s enumerate the states of the
system:
1 state 2 state
AB -
- AB
A B
B A
Total No. of ways it = 4
can be distributed

8. Bose Einstein [BE] Statistics
Characteristics
 Identical
 Indistinguishable
 Zero or integral spin
 Particles are called bosons
 Example: Helium atoms at low
temperature, photons

9. Since the particles are indistinguishable. Both
the particles are labeled as A. Recall that bosons
have integer spin: 0, 1, 2, etc. For Bose statistics
any number of particles can be in one state.
1 state 2 state
AA -
- AA
A A
Total No. of ways it = 3
can be distributed

10. Fermi dirac [FD] Statistics
Characteristics
 Identical
 Indistinguishable
 Half integral spin [eg:1/2, 3/2 etc]
 Particles are called fermions
 Example: electrons,protons,neutrons

11. Since the particles are indistinguishable. Both
the particles are labeled as A. Recall that bosons
spin: 1/2, 3/2, etc. According to the Pauli
exclusion principle, no more than one particle
can be in any one single particle state.
1 state 2 state
A A
Total No. of ways it = 1
can be distributed

12. Questions
1. Define statistical mechanics
2. Mention the types of statistical mechanics
3. Explain the drawback of classical statistics
4. Mention the characteristics of MB statistics
5. Mention the characteristics of FD statistics
6. Mention the characteristics of BE statistics
7. Define pauli’s exclusion principle