# Student Probability Seminar

#### The Thermodynamic Limit: A Mathematical Perspective

**Speaker:**
Aukosh Jagannath

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, December 10, 2013, 3:30 p.m.

**Synopsis:**

One of the key ideas of 19th century thermal physics is that heat can perform of work and that it is related to a quantity called entropy. Boltzmann gave a statistical intepretation of entropy as the log of the multiplicity of states, which is supposed to correspond to physical entropy in the “thermodynamic limit” (as the number of particles tends to infinity). Predictions are then made that reality will chose configurations with maximal entropy at equilibrium. I will make these ideas precise using the language of large deviations, hopefully convicing you that the rate function is the intensive entropy. I will then use this language to analyse the phenomenon of ferromagnetism. With the remaining time I will explain the Dobrushin-Lanford-Ruelle theory of gibbs measures in the thermodynamic limit