Statistical Mechanics book pdf is written by RK Pathria and Paul D. Beale. The book covers all topics from classical as well as quantum statistics. The language is student-friendly and good for developing concept on statistical mechanics. It also includes computational statistics, with Monte Carlo simulation. Recommended for anyone interested in the subject, provided you have an idea of basic thermal physics.

The r k pathria statistical mechanics pdf is useful not only in getting knowledge but also for competition exam such as IITJAM, CSIR-NET and other Undergraduate & postgraduate courses.

## Chapter content of statistical mechanics pathria pdf:

The book contains the following chapters and topics.

Chapter 1. The Statistical Busis of Thermodynamics

1.1. The macroscopic and the microscopic states
1.2. Contact between statistics and thermodynamics: physical significance of the number S2(N, V, E)
1.3. Further contact between statistics and thermodynamics
1.4. The classical ideal gas
1.5. The entropy of mixing and the Gibbs paradox
1.6. The “correct” enumeration of the microstates
Problems
Notes

Chapter 2. Elements of Ensemble Theory

2.1. Phase space of a classical system
2.2. Liouville’s theorem and its consequences
2.3. The microcanonical ensemble
2.4. Examples
2.5. Quantum states and the phase space
Problems
Notes

Chapter 3. The Canonical Ensemble

3.1. Equilibrium between a system and a heat reservoir
3.2. A system in the canonical ensemble
3.3. Physical significance of the various statistical quantities in the canonical ensemble
3.4. Alternative expressions for the partition function
3.5. The classical systems
3.6. Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble
3.7. Two theorems-the “equipartition the “virial”
3.8. A system of harmonic oscillators
3.9. The statistics of paramagnetism
3.10. Thermodynamics of magnetic systems: negative temperatures
Problems
Notes

Chapter 4. The Grund Canonical Ensemble

4.1. Equilibrium between a system and a particle-energy
reservoir
4.2. A system in the grand canonical ensemble
4.3. Physical significance of the various statistical quantities
4.4. Exampless
4.5. Density and energy fiuctuations in the grand canonicalensemble: correspondence with other ensembles
Problems
Notes

Chapter 5. Formulation of Quantum Statistics

5.1. Quantum-mechanical cnsemble theory: the density matrix
5.2. Statistics of the various ensembles

A. The microcanonical ensemble
B. The canonical ensemble
C. The grand canonical ensemble

5.3. Examples

A. An electron in a magnetic field
B. A frce particle in a box
C. A linear harmonic oscillator

5.4. Systems composed of indistinguishable particles
5.5. The density matrix and the partition function of a system of free particles
Problems
Notes

Chapter 6. The Theory of Sinmple Gases

6.1. An ideal gas in a quantum-mechanical microcanonical ensemble
6.2 An ideal gas in other quantum-mechanical ensembles
6.3 Statistics of the occupation numbers
6.4. Kinetic considerations
6.5.Gaseous systems composed of molecules with internal
motion

A. Monatomic molecules
B. Diatomic molecules
C. Polyatomic molecules

Problems
Notes

Chapter 7. weal Bose Systems

7.1. Thermodynamic behavior of an ideal Bose gas
7.2. Thermodynamics of the black-body radiation
7.3. The field of sound waves
7.4. Inertial density of the sound field
7.5. Elementary excitations in liquid helium II –
Problems
Notes

Chapter 8. Ideal Fermi Systems

8.1. Thermodynamic behavior of an ideal Fermi gas
8.2. Magnetic behavior of an ideal Fermi gas

A. Pauli paramagnetism
B. Landau diamagnetism

8.3. The electron gas in metals

A. Thermionic emission (the Richardson effect)
B. Photoelectric emission (the Hallwachs effect)

8.4. Statistical equilibrium of white dwarf stars
8.5. Statistical model of the atom
Problems
Notes

Chapter 9. Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions

9.1. Cluster expansion for a classical gas
9.2. Virial expansion of the equation of state
9.3. Evaluation of the virial coefficients
9.4. General remarks on cluster expansions
9.5. Exact treatment of the second virial coefficient
9.6. Cluster expansion for a quantum-mechanical system
Problems
Notes

Chapter 10. Statistical Mechanics of Interacting Systems: The Method of Quantized Fields

10.1. The formalism of second quantization
10.2. Low-temperature behavior of an imperfect Bose gas
10.3. Low-lying states of an imperfect Bose gas
10.4. Energy spectrum of a Bose liquid
10.5. States with quantized circulation
10.6. Quantized vortex rings and the breakdown of superfluidity
10.7. Low-lying states of an imperfect Fermi gas
10.8. Energy spectrum of a Fermi liquid: Landau’s phenomenological theory
Problems
Notes

Chapter 11. Phase Transitions: Criticality, Universality and Scaling
11.1. General remarks on the problem of condensation
11.2. Condensation of a van der Waals gas
11.3. A dynamical model of phase transitions
11.4. The lattice gas and the binary alloy
11.5. Ising model in the zeroth approximation
11.6. Ising model in the first approximation
11.7. The critical exponents
11.8. Thermodynamic inequalities
11.9. Landau’s phenomenological theory
11.10. Scaling hypothesis for thermodynamic functions
11.11. The role of correlations and fluctuations
11.12. The critical exponents v and n
11.13. A final look at the mean field theory
Problems
Notes

Chapter 12. Phase Transitions: Exact (or Almost Exact) Results for the Various Models

12.1. The Ising model in one dimension
12.2. The n-vector models in one dimension
12.3. The Ising model in two dimensions
12.4. The spherical model in arbitrary dimensions
12.5. The ideal Bose gas in arbitrary dimensions
12.6. Other models
Problems
Notes

Chapter 13. Phase Transitions: The Renormalization Group Approach

13.1. The conceptual basis of scaling
13.2. Some simple examples of renormalization

A. The Ising model in one dimension
B. The spherical model in one dimension
C. The Ising model in two dimensions

13.3. The renormalization group: general formulation
13.4. Applications of the renormalization group

A. The Ising model in one dimension
B. The spherical model in one dimension
C. The Ising model in two dimensions
D. The e-expansion
E. The 1/n expansion
F. Other topics

13.5. Finite-size scaling

Case A : T ≳ Tc (∞)
Case B : T ≃ Tc (∞)
Case C : T < Tc (∞)

Problems
Notes

Chapter 14. Fluctuations
14.1. Thermodynamic fluctuations
14.2. Spatial correlations in a fluid
14.3. The Einstein-Smoluchowski theory of the Brownian
motion
14.4. The Langevin theory of the Brownian motion
14.5. Approach to equilibrium: the Fokker-Planck equation
14.6. Spectral analysis of fluctuations: the Wiener-Khintchine theorem
14.7. The fluctuation- dissipation theorem
14.8. The Onsager relations
Problems
Notes

APPENDIXES

A. Influence of boundary conditions on the distribution of
quantum states
B. Certain mathematical functions
Stirling’s formula for v!
The Dirac δ-function
C. “Volume” and “surface area” of an n-dimensional sphere of radius R
D. On Bose-Einstein functions
E. On Fermi – Dirac functions
F. On Watson functions
Notes

BIBLIOGRAPHY
INDEX