## Cours Ecole Doctorale: From Dynamics to Thermodynamics

Written by Stefano OLLA no commentsCours d'école doctorale de Stefano Olla

**FROM DYNAMICS TO THERMODYNAMICS**

`5,9,10,12 Avril
14 h - 17 h
Salle C
Université Paris Dauphine - PSL`

This course is an elementary introduction to Thermodynamics and Statistical Mechanics. The aim is to explain the main ideas in few concrete models, more than constructing a general theory.

In the first part of the course, the `principles of thermodynamics’ are introduced, and it is explained how these principles can be deduced from the microscopic dynamics of molecules through space-time macroscopic limits. Thermodynamics is obtained as macroscopic theory, i.e., valid on macroscopic space-time scales, while statistical mechanics provides the microscopic model. This means that the objects of thermodynamics are those macroscopic complex systems that satisfy the thermodynamic principles, while statistical mechanics explains how this complexity arise from dynamics of systems with a very large number of components. The central point of this connection is the identification of the thermodynamic entropy, a function of the thermodynamic macroscopic equilibrium states, introduced by Clausius using Carnot cycles, with the Boltzmann definition of entropy in statistical mechanics, as logarithm of the number of microstates corresponding to the given macroscopic state. Boltzmann and Planck discovered this identification at the end of 19th century, but in order to understand it, we need to obtain the thermodynamic transformations constituting the Carnot cycle, isothermal and adiabatic, from the microscopic dynamics through a scaling limit procedure.

This aspect differentiates this course from more classical courses in statistical physics, where only the equilibrium properties of the systems are studied.

As classical thermodynamics concerns transformations from an equilibrium state to another, in the second part of the course I will illustrate how some ideas generalize to transitions between non-equilibrium stationary states.