The Jarzynski equality holds when the initial state is a Boltzmann distribution (e.g. the system is in equilibrium) and the system and environment can be described by a large number of degrees of freedom evolving under arbitrary Hamiltonian dynamics. The final state does not need to be in equilibrium. (For example, in the textbook case of a gas compressed by a piston, the gas is equilibrated at piston position A and compressed to piston position B ; in the Jarzynski equality, the final state of the gas does not need to be equilibrated at this new piston position).