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1¿ù 19ÀÏ ¿ÀÈÄ 2½Ã - 4½Ã (¿¬»ç À¯ÇöÀç)
1¿ù 20ÀÏ ¿ÀÈÄ 2½Ã - 4½Ã (¿¬»ç À¯ÇöÀç)

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¹é¿ëÁÖ (¼­¿ï´ë, ¹°¸®Ãµ¹®ÇкÎ) Introduction to statistical mechanics

ÃÊ·Ï: Using probabilities to account for the effects of uncontrolled or unobservable variables, statistical mechanics bridges the gap between microscopic and macroscopic physics. This lecture is an introduction to the theoretical framework and basic applications of equilibrium statistical mechanics, covering the following topics:

1. Thermodynamic ensembles

- Derivations from the fundamental postulate of statistical mechanics

- Principle of maximum entropy: an alternative Bayesian perspective

- Ensemble equivalence

2. Classical Boltzmann statistics

- Classical ideal gas

- Equipartition theorem

3. Quantum statistics

- Fermi-Dirac statistics

- Bose-Einstein statistics

4. Phase transitions

- Liquid-gas phase transition

- Ising model

À¯ÇöÀç (ÇÑ°æ´ë, ÀÀ¿ë¼öÇаú) Statistical mechanics: from the mathematical viewpoints

ÃÊ·Ï: In these lectures we discuss the statistical mechanics from the mathematical viewpoints. Specifically, we focus on the lattice models. Typical examples are the Ising model and the lattice gas model. The lectures are focused on: 1. Characterization of Gibbs measures, 2. Phase transitions, 3. Some applications. In the first two lectures we will discuss the Gibbs measures. Given an interaction, the equilibrium states, or the Gibbs measures, for the interaction are characterized in a couple of (equivalent) ways. Analytically, a Gibbs measure is characterized by tangent functionals to a (convex) function, the pressure. The variational principle is also a key tool to analyze the Gibbs measures. Rather probabilistically, the Gibbs measures are defined to be the measures that satisfy the DLR (Dobrushin-Lanford-Rulle) conditions. Vaguely speaking, it says that if you take a conditional expectation of the ¡®equilibrium measure¡¯ to any sub-sigma-algebra on the outside of a local system, the inside has a density of Boltzmann factor. In the 3rd lecture, we will discuss the phase transitions through symmetry breaking. In the final lecture, we will discuss some of the applications of the Gibbs measures.


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