**Chris
Jarzynski**

**SYSTEMS
DRIVEN FAR AWAY FROM EQUILIBRIUM**

These lectures will present an introduction to the statistical physics of systems driven away from thermal equilibrium. Following a brief review of the relevant macroscopic thermodynamics, I will turn to microscopic systems, for which statistical fluctuations are relevant. I will describe theoretical and experimental developments over the past decade or so, which have established that far-from- equilibrium statistical fluctuations unexpectedly encode equilibrium thermodynamic information about the system under consideration. In particular, distributions of nonequilibrium work values reveal equilibrium free energy differences. These lectures will focus primarily on the theoretical foundations of these nonequilibrium work relations, using both Hamiltonian and stochastic equations of motion to model the microscopic evolution of the system. I will attempt to place these results in their proper context, by establishing connections to Onsager's formulation of linear response theory, the Feynman-Kac theorem of stochastic processes, as well as more recent entropy fluctuation theorems. As time permits, I will also discuss exactly solvable models that illustrate these results, convergence difficulties that arise in practical applications, and recent development aimed at overcoming these difficulties.