Chemistry

VALENTINA MIGLIORATI
PAOLA D'ANGELO

The course of Statistical Thermodynamics intends to provide the skills necessary for
the use of statistical thermodynamics and its applications. In particular, at the end of
the course the student will have acquired the basic knowledge of both classical and
quantum statistical mechanics, he will know the properties of the different types of
ensembles and he will be able to establish in each case study which ensemble to
apply. The student will have to demonstrate autonomy in learning, as well as critical
judgment on the assimilated concepts. The student is expected to have the ability to
frame the problem under examination in the right context, to know how to choose
the most suitable models for the study of the proposed systems, demonstrating the
ability to apply the skills acquired.

The course of Statistical Thermodynamics intends to provide the skills necessary for the use of statistical thermodynamics and its applications. In particular, at the end of the course the student will have acquired the basic knowledge of both classical and quantum statistical mechanics, he will know the properties of the different types of ensembles and he will be able to establish in each case study which ensemble to apply. The student will have to demonstrate autonomy in learning, as well as critical judgment on the assimilated concepts. The student is expected to have the ability to frame the problem under examination in the right context, to know how to choose the most suitable models for the study of the proposed systems, demonstrating the ability to apply the skills acquired.

Basic knowledge of Thermodynamics. Fundamental elements of Quantum Mechanics.

Definition of Ensemble. Liouville theorem. Microcanonical ensemble. Ergodic hypothesis. Statistical entropy. Internal energy and absolute temperature. External variables and generalized forces. The chemical potential. First law of thermodynamics. The entropy of an ideal gas. Calculation of the probability distribution of a physical quantity. Canonical ensemble. Thermodynamic functions of the canonical Ensemble. The canonical ensemble for perfect gases.
Quantum Statistical Mechanics. Elements of quantum mechanics: the wave function, expectation values, results of experimental measurements. Postulate of a priori equal probability. Postulate of random phases. Time evolution of sets. Continuous generalization. Microcanonical and canonical ensemble. The Pauli exclusion principle and Symmetrization postulate. Entropy: quantum form and number of states. Boltzmann's H theorem. Maxwell distribution. Principle of Equipartition of Energy. Grand Canononical Ensemble. Grand canonical ensemble for perfect gases. Grand Canonical Ensemble in Quantum Statistical Mechanics. The fluctuations. Fermi-Dirac distribution. The Fermi level. Heat capacity of a free electron gas at low temperatures. Bose-Einstein distribution. Einstein's condensation.

To prepare the exam, refer to all the didactic material (Slides) made available.
Recommended books: Statistical Mechanics, K. Huang Zanichelli (1997)

Lessons take place in person

Attendance is optional but highly recommended due to the complexity of the treated topics.

The exam will consist of an oral exam in which you will be asked to illustrate the different topics of the course.

Questions about the different topics of the course.