1. Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski’s Equality Simon-Shlomo Poil 9.december 2005 Single Molecule Biophysics J. Liphardt et al., Science, 296, 5574, 1832-1835 (2002)

2. Equilibrium / Nonequilibrium Thermodynamic Irreversible processes drive a Nonequilibrium system towards an Equilibrium system Equilibrium systems have one uniform temperature, and state functions of energy and entropy - e.g. U = U(T,V,N) and S = S(T,V,N) In Nonequilibrium systems the energy and entropy need to be described using energy and entropy densities.

3. Jarzynski’s equality or normal C. Jarzynski 1997 N = # of work trajectories z = order parameter

4. Experiment Reversible slow switching rate 2 to 5 pN/s Irreversible fast switching rates 34 and 52 pN/s Compare three different estimates Average work Fluctuation-dissipation Jarzynski’s estimate p5abc

5. Force-extension curves

6. Reversible Irreversible green, 34pN/s Red, 52 pN/s

7. Jarzynski’s equality as a sum If the distribution is Gaussian, (near equilibrium state) To use Jarzynski’s equality experimentally; fluctuations should be below K b T

8. Convergence of Jarzynski

9. Conclusion and are equal in near-equilibrium and unequal in far-equilibrium. Jarzynski gives the same at the two different irreversible switching rates (within 0.3 K b T ) The difference between reversible and irreversible work is less than 0.6 K b T Jarzynski overestimate where the work dissipation is largest Reversible : Jarzynski :