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Quantum work fluctuation theorems are known to hold when the work is definedas the difference between the outcomes of projective measurements carried outon the Hamiltonian of the system at the initial and the final time instants ofthe experimental realization of the process. A recent study showed that thetheorem breaks down if the measurement is of a more general nature, i.e. if apositive operator valued measurement is used, and the deviation vanishes onlyin the limit where the operators become projective in nature. We study a simpletwo-state system subjected to a unitary evolution under a Hamiltonian that islinearly dependent on time, and verify the validity of the above statement. Wefurther define a weak value of work and show that the deviation from the exactwork fluctuation theorems are much less in this formalism.

Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements