1 / 55

Experimental results on the fluctuations in two out of equilibrium systems

Firenze, 16 February 2009. Experimental results on the fluctuations in two out of equilibrium systems S. Joubaud , P.Jop, A. Petrossyan and S.C. Laboratoire de Physique, ENS de Lyon, UMR5672 CNRS. Outline. Motivation for experiments.

orla-greene
Download Presentation

Experimental results on the fluctuations in two out of equilibrium systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Firenze, 16 February 2009 Experimental results on the fluctuations in two out of equilibrium systems S. Joubaud , P.Jop, A. Petrossyan and S.C. Laboratoire de Physique, ENS de Lyon, UMR5672 CNRS

  2. Outline • Motivation for experiments. • Fluctuations of injected power in an harmonic oscillator. • Fluctuation Theorems for work, heat and total entropy. • Injected power in the stochastic resonance • Conclusions

  3. Experimental study of Fluctuations in Mechanical Systems Motivation • Study of thermodynamics laws in weakly out of equlibrium systems.For example the application of Fluctuation Dissipation Theorem (FDT) in aging materials • Applications of fluctuation theorems to estimate thermal losses in these systems. • Estimate the reversible and irreversible part of the work done by an external force on the system. Check the hypothesis done to prove FT Test in experiments the analytical and numerical studies on FT What is the good variable to look at ?

  4. brass wire gold mirror The system of interest Torsion pendulum

  5. Experimental set up and the interferometer

  6. External Forcing

  7. Equation of motion In Fourier space The thermal fluctuation powerspectral density is given by FDT

  8. Typical Fluctuation spectra Spectrum of the torsion pendulum made by a brass wire and a mirror Spectrum of the torsion pendulum inside a viscous oil

  9. Work during periodic forcing

  10. PDF of the work

  11. Energy Balance (I) Sekimoto K, Progress of Theoretical Phys.supplement (130), 17 (1998).

  12. Energy Balance (II) Sekimoto K, Progress of Theoretical Phys.supplement (130), 17 (1998).

  13. PDF of heat

  14. PDF of the work and of the heat

  15. Stationary State Fluctuation Theorem(SSFT) Fluctuation Theorem fixes the symmetry of P(X) around zero

  16. SSFT periodic forcing: W

  17. SSFT periodic forcing: S

  18. SSFT periodic forcing: Q Energy disipated in a time t

  19. SSFT periodic forcing: S for Q

  20. Linear forcing

  21. t ti Transient and Steady State Fluctuation Theorem TFT SSFT t

  22. TFT

  23. SSFT

  24. S(t) for the SSFT

  25. Theoretical description What are the fluctuations of Qwhen the system is out of equilibrium ? Linear ramp torque

  26. Theoretical description Langevin Equation

  27. Theoretical description: Fluctuation Theorem for W

  28. Theoretical description: Fluctuation Theorem for Q

  29. Theoretical description: Fluctuation Theorem for Q

  30. Trajectory dependent entropy U. Seifert, Phys. Rev. Lett., 95, 040602, (2005), for Langevin dynamics A. Puglisi, L. Rondoni, A. Vulpiani, J. Stat. Mech.: Theory and Experiment, P08010,(2006) for Markov process

  31. Trajectory dependent entropy

  32. Trajectory dependent entropy

  33. Fluctuations of the total entropy

  34. FT for total entropy FT for total entropy

  35. Conclusions • We have experimentally perturbed an harmonic oscillator very close to equilibrium. • We have computed and measured the finite time corrections for SSFT and TFT. • The ‘’ trajectory dependent entropy ‘’ has been computed • We have checked that for the total entropy SSFT is verified for all times. • We have shown that in this specific example the ‘’total entropy’’ takes into account only the entropy produced by the external driving and does not take into account the entropy fluctuations at equilibrium.

  36. The stochastic resonance and Fluctuatio Theorem P.Jop. A. Petrosian, S. Ciliberto, EPL March 2008

  37. Camera rapide AOD 75 MHz Multiple optical traps

  38. Examples of traps

  39. The non linear potential

  40. The non linear potential f=0.1Hz

  41. Stochastic Resonance

  42. Fluctuations of W and Q at Stochastic Resonance Stochastic work Classical work Heat

  43. PDF of the Work at various frequencies f=0.1Hz f=0.05Hz f=2Hz f=0.375Hz

  44. Fluctuation Theorem for Ws f=0.25Hz

  45. PDF of DU

  46. Fluctuation Theorem for Q

  47. Slope at the origin

  48. Theoretical comparison I A. Imparato, P. Jop, A. Petrosyan and S. Ciliberto, J. Stat. Mech. (2008) P10017 PDF of the work computed on a single period : (initial phase=0) (averaged over different initial phases) Experimental data Theoretical prediction based on Fokker-Planck equation

More Related