What does this equation mean?

The next structural advance did not concern the demon at all; it concerned a much older and more general problem — how to extract equilibrium information from a process driven arbitrarily far from equilibrium. In 1997, Christopher Jarzynski published “Nonequilibrium Equality for Free Energy Differences” in Physical Review Letters [ 3 ] . The Jarzynski equality states that if a system is driven from one equilibrium state to another along some protocol, performing a fluctuating amount of work W on each repetition, the equilibrium free energy difference $\Delta$ F between the two states can be recovered exactly from an exponential average over the work distribution: $\left\langle e^{-W/k_B T} \right\rangle = e^{-\Delta F/k_B T}$. This is a striking claim on its face: it says a quantity defined only for reversible, quasistatic processes — a free energy difference — can be computed from measurements of an irreversible process, no matter how fast or violent the driving, provided enough repetitions are averaged. Two years later, Gavin Crooks derived a closely related and in some respects more general result, the Crooks fluctuation theorem, in “Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences,” published in Physical Review E in 1999 [ 4 ] . Crooks’s relation compares the probability of observing work W in a forward protocol to the probability of observing -W in the corresponding time-reversed protocol: