Fluctuation theorems for quasistatic work

When a thermally isolated system performs a driving process in the quasistatic regime, its variation of average energy is equal to its quasistatic work. Even though presenting this simple definition, few attempts have been made to describe such quantity from the fluctuation theorem point of view. In this work, based on Jarzynski’s equality, four forms of such equality are deduced. To corroborate the result, a relation with the strong inequality $⟨W⟩\ge ⟨W_{\mathrm{q}\mathrm{s}}⟩$ is pursued. It is concluded in the end that any of the fluctuation theorems deduced cannot derive such a postulate. Also, no contradiction is observed if the strong inequality breaks down.