**CHM 630: Advanced Statistical Mechanics**** ****(4)**

**Prerequisites: **CHM322/CHM642/PHY303, CHM421/PHY306 or their equivalent

*Basic postulates and ensembles:* Distributions, partition functions and calculation of thermodynamic properties in various ensembles.

*Classical Statistical Mechanics:* Classical partition function (rotational, vibrational and translational) as the high-temperature limit of its quantum counterpart, microscopic equations of motion, phase space, phase space vectors and Liouville’s theorem, the Liouville equation and equilibrium solutions, ergodic theory.

*Theory of imperfect gases:* Cluster expansion for a classical gas, evaluation of cluster integrals, virial explansion of the equation of state, evaluation of the virial coefficients, law of corresponding states.

*Theory of the liquid state:* Definition of distribution and correlation functions, radial distribution function, Kirkwood integral equation, potential of mean force and the superposition approximation, Ornstein-Zernicke equation, Percus-Yevick and hypernetted-chain approximations., density expansion of the pair functions, perturbation theory of the van der Waals’ equation.

*Critical phenomena:* Critical behaviour of the van der Waals equation, Ising model, lattice-gas model and binary alloys, broken symmetries, mean-field theories, Landau-Ginsburg theory, scaling and universality, introduction to renormalization group theory.

*Suggested Readings *:

- Chandler, D.,
*Introduction to Modern Statistical Mechanics*, Oxford,**1987**. - McQuarrie, D. A.,
*Statistical Mechanics*, University Science Books,**2000**. - Hansen, J. P., and McDonald, I. R.,
*Theory of Simple Liquids,*Ed. 3rd, Academic Press,**2006**. - Pathria, R. K.,
*Statistical Mechanics*, Ed. 2nd, Butterworth-Heinemann,**1996**. - Stanley, H. E.,
*Introduction to Phase Transitions and Critical Phenomena*, Oxford,**1971**.

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