Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski’s Equality Simon-Shlomo Poil 9.december 2005 Single Molecule.

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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, (2002)

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.

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

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

Force-extension curves

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

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

Convergence of Jarzynski

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 :