Generalized Jarzynski Equality
  The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to the initial equilibrium partition functions of the system at that fixed temperature. It thus relates two thermal equilibrium quantum states. Here a generalization is given that relates any two quantum states of a system. 
Don N. Page
hep-th cond-mat.stat-mech quant-ph