Quantum states and complexions. Microcanonical ensemble. Maxwell-Boltzmann distribution law. Partition function. Entropy. Ensemble averages. Statistical approach to thermodynamic properties. Canonical ensemble. Quantum-mechanical calculation of partition functions. Specific heat in gases and solids. Ideal and regular mixtures. Equilibrium constants. Phase space. Phase integral. Bose-Einstein and Fermi-Dirac statistical distribution laws. Nonequilibrium thermodynamics. Computer training.
Title: Statistical Thermodynamics
Author: Bernard J. McClelland
Publisher: Chapman and Hall, 1973
Title: Statistical Thermodynamics
Author: Normand M. Laurendeau
Publisher: Cambridge University Press, 2005
Title: Free Energy Calculations (Theory and Applications in
Chemistry and Biology)
Editors: Christophe Chipot, Andrew Pohorille
Springer Series in CHEMICAL PHYSICS (Volume 86 2007)
Learning Objectives
The aim of the course is to provide basic knowledge about theoretical chemistry addressing specific issues of statistical mechanics and thermodynamics concerning equilibrium and nonequilibrium processes. Specifically, the aim is to explore several aspects related to the detailed relation between the quantum nature of a system and its thermodynamical properties, starting from fundamental statistical concepts associated with the fashion of populating quantum states. Furthermore, modern theories will be discussed, which provide a precise statistical statement of the second principle of thermodynamics. Optionally, it will be possible to perform a computer training to compute thermodynamical properties of a system exploiting molecular data obtained by means of quantum chemistry calculations.
Prerequisites
The knowledge acquired in the part pf statistical mechanics of the course of "Advanced Chemical-Physics" (B012815) is very useful for a fruitful participation to the course.
Teaching Methods
Lessons of theory (5 CFU) will be accompanied to computer practice (1 CFU).
Type of Assessment
The exam is oral and consists of a deep discussion of a topic presented in the lectures and communicated to the student by no more than 24 hours before the discussion. The computer training, if done, will be evaluated and contribute to the final result by no more than 20%.
Course program
Quantum states and complexions. Concepts of distribution and distribution number. Permutations. Number of complexions for a system of independent and distinguishable molecules (degenerate and non-degenerate cases). Probability of a distribution. Microcanonical ensemble. Maxwell-Boltzmann distribution law. Molecular partition function. Average values of molecular properties. Statistical interpretation of temperature. Entropy. Entropy Boltzmann law. Second principle of thermodynamics. Calculation of thermodynamical properties. Canonical ensemble. Ensemble averages. Ergodic hypothesis. Partition function of a macroscopic system. Canonical ensemble of independent particles. Factorization of the molecular partition function. Maxwell-Boltzmann distribution law for indistinguishable particles (gaseous systems). Translational partition function. State equation of a perfect gas (determination of the Boltzmann constant). Factorization of the internal partition function. Nuclear, electronic, vibrational and rotational partition functions. Specific heats. Einstein model and Debye theory for the specific heat of a crystal. Mixtures. Mixing entropy of ideal liquid and solid solutions and of perfect gases. Statistical calculation of equilibrium constants. Equilibrium constants of simple systems. Phase space. Partition function and phase integral Q in a classic system. Factorization of Q in the phase space. Calculation of Q in simple classic systems. Energy equipartition. Molecular velocities. Bose-Einstein and Fermi-Dirac statistical distribution laws. Electrons in metals. Gas of bosons and Bose-Einstein condensation. Nonequilibrium statistical thermodynamics. Calculation of equilibrium properties from nonequilibrium quantities. Transient fluctuation theorem by Crooks. Jarzynski equality. Statistical statement of the second principle of thermodynamics and of related theorems. Computer training.