Lecture 20: Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble 
Lecture 20: Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble by NPTEL / V. Balakrishnan
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Date Added: November 18, 2010

Lecture Description

Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble
Binomial Distribution
Relative Fluctuation

Course Index

  1. Lecture 1: Mass, Length and Time
  2. Lecture 2: Classical Dynamics
  3. Lecture 3: Harmonic Oscillator
  4. Lecture 4: Harmonic Oscillator
  5. Lecture 5: Dimensional dynamical systems
  6. Lecture 6: Dimensional dynamical systems
  7. Lecture 7: The Principles of the Equations of Motion
  8. Lecture 8: Maxwell's Equations
  9. Lecture 9: Lagrangian for a charged particle in a EM field
  10. Lecture 10: Lagrangian and Hamiltonian Dynamics
  11. Lecture 11: Hamiltonian Systems
  12. Lecture 12: Integrability of Hamiltonian Systems
  13. Lecture 13: Emmy Noether, Symmetry, Invariance and Conservation Laws
  14. Lecture 14: Isotropic Oscillators, The Kepler Problem, Introduction to Statistical Physics
  15. Lecture 15: Chaotic Dynamics
  16. Lecture 16: Exponential Divergencies, Lyapunov Exponent, Bernoulli Map and Frobenius-Perron Equation
  17. Lecture 17: Lyapunov Exponent, Baker's Map, Arnold's cat map, Gauss continued fraction map
  18. Lecture 18: Questions & Answers
  19. Lecture 19: Questions & Answers
  20. Lecture 20: Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble
  21. Lecture 21: Microcanonical Ensemble: Stirling's Formula, Poisson Distribution
  22. Lecture 22: Microstates of particles, Entropy, Density of States, Thermodynamics
  23. Lecture 23: Euler Relation, Enthalpy, Helmholtz / Gibbs Free Energies, Grand Potential, Field / State Variables, Gas Law
  24. Lecture 24: Density of States, Boltzmann/Gibbs Factor
  25. Lecture 25: Thermodynamics of Ideal Gases and its Statistic Mechanics
  26. Lecture 26: Probability and Maxwellian Distributions, Moment generating function, Excess Kurtosis, Levy distributions
  27. Lecture 27: Maxwellian distributions, Gunbel, Weibull & Frechet distribution, Phase Diagrams
  28. Lecture 28: Phase Diagrams, Model of Paramagnetism, dipole moment, Weiss molecular field theory
  29. Lecture 29: Ferromagnetism, spontaneous magnetization, Landau Theory
  30. Lecture 30: Landau Theory and critical exponents, Thermodynamic relations, Continuum limit of random walk
  31. Lecture 31: Questions & Answers
  32. Lecture 32: Lie Groups, homomorphism, kernel
  33. Lecture 33: Groups, compact and non-compact groups, Universal covering group
  34. Lecture 34: Group of proper rotation in 3D, Parametrization by Euler angles, unitary matrices, Noether's theorem
  35. Symmetry, Invariance and Conservation laws (Noether's theorem), Principles of Relativity
  36. Lecture 36: Lorentz invariance, Riemannian manifold, metric tensors, d'Alembert operator
  37. Lecture 37: EM Field tensor, dual tensor, Levi-Civita symbol in 4D, Lorentz transformations, time/space-like vectors
  38. Lecture 38: Lorentz transformations in EM fields

Course Description

Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras. Among the topics in the lectures are:

- Mass, Length and Time
- Classical Dynamics
- Harmonic Oscillator
- Harmonic Oscillator
- Dimensional dynamical systems
- Dimensional dynamical systems
- The Principles of the Equations of Motion
- Maxwell's Equations
- Lagrangian for a charged particle in a EM field
- Lagrangian and Hamiltonian Dynamics
- Hamiltonian Systems
- Integrability of Hamiltonian Systems
- Emmy Noether, Symmetry, Invariance and Conservation Laws
- 2D Isotropic Oscillators, The Kepler Problem, Introduction to Statistical Physics
- Integrable Systems: Periodic, Quasiperiodic, Ergotic, Mixing Motion, Exponential Instability, global - exponential instability
- Lyapunov Exponent
- Intermitency
- E.N. Lorenz
- Exponential Divergencies, Lyapunov Exponent, Bernoulli Map, Frobenius-Perron Equation
- Lyapunov Exponent, Baker's Map, Arnold's cat map, Gauss continued fraction map
- Statistical Mechanics: Isolated Systems, Fundamental Postulate of Equilibrium, Microcanonical Ensemble
- Binomial Distribution
- Relative Fluctuation
- Thermodynamics of Ideal Gases and its Statistic Mechanics
- Boltzmann's Formula
- Probability and Maxwellian Distributions, Moment generating function, Excess Kurtosis, Lévy alpha-stable distributions
- J.A. Shabat and J.D. Tamarkin, "The problem of moments"
- Maxwellian distributions, Gunbel, Weibull & Frechet distribution, Phase Diagrams
- Phase Diagrams, Model of Paramagnetism, dipole moment, Weiss molecular field theory
- Ferromagnetism, spontaneous magnetization, Landau Theory
- Landau Theory and critical exponents, Thermodynamic relations, Continuum limit of random walk
- Lie Groups, homomorphism, kernel
- Group of proper rotation in 3D, Parametrization by Euler angles, unitary matrices, Noether's theorem
- Symmetry, Invariance and Conservation laws (Noether's theorem), Principles of Relativity
- Lorentz invariance, Riemannian manifold, metric tensors, d'Alembertian operator
- EM Field tensor, dual tensor, Levi-Civita symbol in 4D, Lorentz transformations, time-like and space-like vectors
- Lorentz transformations in EM fields

For more details on NPTEL visit http://nptel.iitm.ac.in

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