Abstract
The third lecture dealt with Jarzinsky's and Crooks' relations and their generalizations. Because of fluctuations on the microscopic scale, the work that has to be done by a system, when exactly the same experimental protocol is repeated, fluctuates. For example, the precise amount of work required to change the volume of a gas by moving a piston is the sum of the elementary work done each time the piston collides with a gas molecule. For a system at equilibrium, this work fluctuates when exactly the same experiment is repeated, simply because the initial microscopic configuration of the gas changes from one experiment to the next. Assuming the system is initially at equilibrium, the Jarzynski and Crooks relations relate certain averages of work functions (the average of an exponential of work in the case of the Jarzynski relation) to the difference in free energy or entropy between the initial and final states.
After showing how the second principle derives from these relations, the lecture continued with their demonstration in the case of stochastic dynamics, their illustration in the case of the Szilard machine, their generalization to non-equilibrium stationary regimes (Hatano-Sasa relation) and to situations for which we have partial information on the system (Sagawa-Ueda relations).
