Statistics of work and fluctuation theorems for microcanonical initial states

Work performed on a system in a microcanonical state by changes in a control parameter is characterized in terms of its statistics. The transition probabilities between eigenstates of the system Hamiltonians at the beginning and the end of the parameter change obey a detailed balance-like relation from which various forms of the microcanonical fluctuation theorem are obtained. As an example, sudden deformations of a two-dimensional harmonic oscillator potential are considered, and the validity of the microcanonical Jarzynski equality connecting the degrees of degeneracy of energy eigenvalues before and after the control parameter change is confirmed.