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Simon-Shlomo Poil 9.december 2005 Single Molecule Biophysics

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

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Simon-Shlomo Poil 9.december 2005 Single Molecule Biophysics

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  1. Equilibrium Information fromNonequilibrium Measurementsin an Experimental Test ofJarzynski’s Equality J. Liphardt et al., Science, 296, 5574, 1832-1835 (2002) Simon-Shlomo Poil 9.december 2005 Single Molecule Biophysics

  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 normal or 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 p5abc • Compare three different estimates • Average work • Fluctuation-dissipation • Jarzynski’s estimate

  5. Force-extension curves

  6. Reversible Irreversiblegreen, 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 KbT

  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 KbT ) • The difference between reversible and irreversible work is less than 0.6 KbT • Jarzynski overestimate where the work dissipation is largest Reversible : Jarzynski :

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