Skip to main content
SpringerLink
Log in

Test of the Fluctuation Relation in Lagrangian Turbulence on a Free Surface

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The statistics of velocity divergence are studied for an assembly of particles that float on a closed turbulent fluid. Under an appropriate definition of entropy, the two-dimensional Lagrangian velocity divergence of a particle trajectory represents the local entropy rate \({\dot{S}}\) , a random variable in time. The statistics of this rate, measured in the Lagrangian frame, are collected over a wide range of values. This permits a severe test of the fluctuation relation (FR) over a range that exceeds prior experiments, out to a regime beyond which the FR no longer holds. Notably, the probability density functions (PDF) of the dimensionless divergence σ τ are strongly non-Gaussian.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aumaitre, S., Fauve, S., McNamara, S., Poggi, P.: Power injected in dissipative systems and fluctuation theorems. Europhys. J. B 19, 449 (2001)

    ADS  Google Scholar 

  2. Bandi, M.M., Goldburg, W.I., Cressman, J.R.: Measurement of entropy production rate in compressible turbulence. Europhys. Lett. 76, 595 (2006)

    Article  ADS  Google Scholar 

  3. Boffetta, G., Davoudi, J., Eckhardt, B., Schumacher, J.: Lagrangian tracers on a surface flow: the role of time correlation. Phys. Rev. Lett. 93, 134–501 (2004)

    Article  Google Scholar 

  4. Boffetta, G., DeLillo, F., Gamba, A.: Large scale inhomogeneity of inertial particles in turbulent flows. Phys. Fluids 16, L20 (2004)

    Article  ADS  Google Scholar 

  5. Bonetto, F., Chernov, N.I., Lebowitz, J.L.: (Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium. Chaos 8, 823 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Bonetto, F., Gallavotti, G., Garrido, P.L.: Chaotic principle: an experimental test. Phys. D 105, 226 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bonetto, F., Gallavotti, G., Gentile, G.: A fluctuation theorem in a random environment. Preprint nlin.CD/0605001 (2006)

  8. Bonetto, F., Gallavotti, G., Giuliani, A., Zamponi, F.: Chaotic hypothesis, fluctuation theorem and singularities. J. Stat. Phys. 123, 39 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Carberry, D.M., Reid, J.C., Wang, G.M., Sevick, E.M., Searles, D.J., Evans, D.J.: Fluctuations and irreversibility: an experimental demonstration of a second-law-like theorem using a colloidal particle held in an optical trap. Phys. Rev. Lett. 92, 140–601 (2004)

    Article  Google Scholar 

  10. Chetrite, R., Delannoy, J.Y., Gawedzki, K.: Kraichnan flow in a square: an example of integrable chaos. nlin.CD/0606015 (2006)

  11. Ciliberto, S., Garnier, N., Pinton, J.F., Ruiz-Chavarria, R.: Experimental test of the Gallavotti–Cohen fluctuation theorem in turbulent flows. Phys. A 340, 240 (2004)

    Article  Google Scholar 

  12. Ciliberto, S., Laroche, C.: An experimental test of the Gallavotti–Cohen fluctuation theorem. J. Phys. IV (France) 8, 215 (1998)

    Google Scholar 

  13. Cohen, E.G.D.: Dynamical ensembles in statistical mechanics. Phys. A 240, 43 (1997)

    Article  ADS  Google Scholar 

  14. Collin, D., Ritort, F., Jarzynski, C., Smith, S.B., Smith, I.T. Jr., Bustamante, C.: Verification of the crooks fluctuation theorem and recovery of RNA free folding energies. Nature 437, 231 (2005)

    Article  ADS  Google Scholar 

  15. Cressman, J.R., Davoudi, J., Goldburg, W.I., Schumacher, J.: Eulerian and Lagrangian studies in surface flow turbulence. New J. Phys. 6, 53 (2004)

    Article  ADS  Google Scholar 

  16. Crooks, G.E.: Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 2721, 60 (1999)

    Google Scholar 

  17. Denissenko, P., Falkovich, G., Lukaschuk, S.: How waves affect the distribution of particles that float on a liquid surface. Phys. Rev. Lett. 97, 244–501 (2006)

    Article  Google Scholar 

  18. Dorfman, J.R.: An Introduction to Chaos in Nonequilibrium Statistical Mechanics. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  19. Douarche, F., Ciliberto, S., Petrosyan, A.: Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models. J. Stat. Mech. P09011 (2005)

  20. Douarche, F., Ciliberto, S., Petrosyan, A., Rabbiosi, I.: An experimental test of the Jarzynski equality in a mechanical experiment. Europhys. Lett. 70, 593 (2005)

    Article  ADS  Google Scholar 

  21. Evans, D.J., Cohen, E.G.D., Morriss, G.P.: Probability of second law violations in shearing steady states. Phys. Rev. Lett. 71, 2401 (1993)

    Article  MATH  ADS  Google Scholar 

  22. Falkovich, G., Fouxon, A.: Entropy production away from the equilibrium. Preprint nlin.CD/0312033 (2003)

  23. Falkovich, G., Fouxon, A.: Entropy production and extraction in dynamical systems and turbulence. New J. Phys. 6, 11 (2004)

    Article  Google Scholar 

  24. Falkovich, G., Weinberg, A., Denissenko, P., Lukaschuk, S.: Surface tension: floater clustering in a standing wave. Nature 435, 1045 (2005)

    Article  ADS  Google Scholar 

  25. Feitosa, K., Menon, N.: Fluidized granular medium as an instance of the fluctuation theorem. Phys. Rev. Lett. 92, 164–301 (2004)

    Article  Google Scholar 

  26. Gallavotti, G.: Chaotic dynamics, fluctuations, nonequilibrium ensembles. Chaos 8, 384 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Gallavotti, G.: A local fluctuation theorem. Phys. A 263, 39 (1999)

    Article  MathSciNet  Google Scholar 

  28. Gallavotti, G.: Entropy production and thermodynamics of nonequilibrium stationary states. Chaos 14, 680 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. Gallavotti, G., Cohen, E.G.D.: Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 74, 2694 (1995)

    Article  ADS  Google Scholar 

  30. Garnier, N., Ciliberto, S.: Nonequilibrium fluctuations in a resistor. Phys. Rev. E 71, 60–101(R) (2005)

    Article  Google Scholar 

  31. Gentile, G.: A large deviation theorem for Anosov flows. Forum Math. 10, 89 (1999)

    Article  MathSciNet  Google Scholar 

  32. Gilbert, T.: Fluctuation theorem applied to the Nosé–Hoover thermostatted Lorentz gas. Phys. Rev. E. 73, 35–102 (2006)

    Google Scholar 

  33. Goldburg, W.I., Cressman, J.R., Vörös, Z., Eckhardt, B., Schmacher, J.: Turbulence in a free surface. Phys. Rev. E 63, 65–303(R) (2001)

    Article  Google Scholar 

  34. Goldburg, W.I., Goldschmidt, Y.Y., Kellay, H.: Fluctuation and dissipation in liquid-crystal electroconvection. Phys. Rev. Lett. 87, 245–502 (2001)

    Article  Google Scholar 

  35. Jarzynski, C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690 (1997)

    Article  ADS  Google Scholar 

  36. Kurchan, J.: Fluctuation theorem for stochastic dynamics. J. Phys. A: Math. Gen. 31, 3719 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  37. Lebowitz, J., Spohn, H.: A Gallavotti–Cohen type symmetry in the large deviation functional for stochastic dynamics. J. Stat. Phys. 95, 333 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  38. Liphardt, J., Dumont, S., Smith, S.B., Tinoco, I., Bustamante, C.: Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality. Science 296, 1832 (2002)

    Article  ADS  Google Scholar 

  39. Narayan, O., Dhar, A.: Reexamination of experimental tests of the fluctuation theorem. J. Phys. A: Math. Gen. 37, 63 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  40. Ruelle, D.: Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys. 95, 393 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  41. Schuster, H.G., Just, W.: Deterministic Chaos: An Introduction, 4th edn. Wiley, New York (2005)

    MATH  Google Scholar 

  42. Shang, X.D., Tong, P., Xia, K.Q.: Test of steady-state fluctuation theorem in turbulent Rayleigh–Bénard convection. Phys. Rev. E 72, 15–301(R) (2005)

    Article  Google Scholar 

  43. Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J.: Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys. Rev. Lett. 89, 50–601 (2002)

    Google Scholar 

  44. Yeung, P.K., Sawford, B.L.: Random-sweeping hypothesis for passive scalars in isotropic turbulence. J. Fluid. Mech. 459, 129 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    M. M. Bandi & W. I. Goldburg

  2. Center for Nonlinear Studies and Condensed Matter and Thermal Physics Division, MS K764, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    M. M. Bandi

  3. 212 Earth and Engineering Sciences, Pennsylvania State University, University Park, PA, 16802, USA

    J. R. Cressman Jr.

Authors
  1. M. M. Bandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. R. Cressman Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. I. Goldburg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Bandi.

Additional information

This work was supported by the National Science Foundation under grant number DMR-0201805.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bandi, M.M., Cressman, J.R. & Goldburg, W.I. Test of the Fluctuation Relation in Lagrangian Turbulence on a Free Surface. J Stat Phys 130, 27–38 (2008). https://doi.org/10.1007/s10955-007-9355-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-007-9355-4

Keywords

Search

Navigation