The over-line indicates an average over all possible realizations of an external process that takes the system from the equilibrium state A to a new, generally nonequilibrium state under the same external conditions as that of the equilibrium state B. This average over possible realizations is an average over different possible fluctuations that could occur during the process (due to Brownian motion, for example), each of which will cause a slightly different value for the work done on the system. In the limit of an infinitely slow process, the work W performed on the system in each realization is numerically the same, so the average becomes irrelevant and the Jarzynski equality reduces to the thermodynamic equality Δ Δ F = W (see above). Away from the infinitely slow limit, the average value of the work obeys Δ Δ F ≤ ≤ W ¯ ¯ , while the distribution of the fluctuations in the work are further constrained such that e − − Δ Δ F / k T = e − − W / k T ¯ ¯ . In this general case, W depends upon the specific initial microstate of the system, though its average can still be related to Δ Δ F through an application of Jensen's inequality in the JE, viz.