Recently, the development of single molecule manipulation has led new sight into mechanical properties of individual molecules. However, the measurement in experiment drive systém away from equilibrium. How can one extract equilibrium properties? According to the second thermodynamics law, the mechanical work is always larger than the free energy, except that the experiment is performed reversibly or infinitely slowly. However, recently Jarzynski discovered the identity between thermodynamic free energy differences and the irreversible work. Thus one should be able to extract free energy surfaces from the atomic force measurements in repeated pulling single molecule experiments.

In the single molecular force measuring experiment, the sample is moved with a constant speed relative to the cantilever with spring constant k. The position of the cantilever with respect to the sample is recorded. After repeating this measurement a certain times, the free energy profile of the equilibrium systém can be obtained exactly according to Jarzynski's equality. This reconstruction result fits well with the reconstruction curve. Through measuring the pulling force, one can also estimate the free energy profile through integrating. However, this introduces some artifacts and should not be considered accurate.

In another experiment, the free energy profile from Jarzynski's equality is compared with that from fluctuation-dissipation relation. The results show that in reversible process both of them fits well with theoretical predictions for near-equilibrium conditions. In irreversible process, the free energy profile from Jarzynski's equality performs consistently over the entire range, while the free energy profile fails at large extension range. The effect of repeating times is also tested. The results shows that the more times the process repeats, the better the free energy profile recovers.

In conclusion, Jarzynski raised an equality relating the irreversible work to the equilibrium free energy difference. And this is approved by the recently developed single molecule manipulation experiments.

Reference: Gerhard Hummer and Attila Szabo, PNAS, 98, 7, 2001

                 Jan Liphardt etc, Science, 296, 1832, 2002