We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two-state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two-state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental set-up. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.
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