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Thermally induced directed currents in hard rod systems

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Abstract

We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents when the spatially inhomogeneous heat-bath and the periodic potential profile display an appropriate relative phase shift, \({\phi}\) . By comparison with the collisionless limit, we determine the conditions for the most efficient transport among inelastic, elastic and non interacting rods. We show that the situation is complex as, depending on shape of the temperature profile, the current of one system may outperform the others.

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References

  1. Reimann P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361, 57–265 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Van den Broeck C., Meurs P., Kawai R.: From Maxwell demon to Brownian motor. New J. Phys. 7, 10 (2005)

    Article  Google Scholar 

  3. Costantini G., Marconi U.M.B., Puglisi A.: Granular Brownian ratchet model. Phys. Rev. E 75, 061124 (2007)

    Article  ADS  Google Scholar 

  4. Risken H.: The Fokker–Planck Equation: Methods of Solution and Applications, vol. 18. Springer, Berlin (1996)

    Google Scholar 

  5. Gardiner C.W.: Handbook of Stochastic Methods. Springer, Berlin (1985)

    Google Scholar 

  6. Landauer R.: Inadequacy of entropy and entropy derivatives in characterizing the steady state. Phys. Rev. A 12, 636–638 (1975)

    Article  ADS  Google Scholar 

  7. Hänggi P., Bartussek R.: Brownian rectifiers: how to convert Brownian motion into directed transport. In: Parisi, J, Müller, S., Zimmermann, W (eds) Nonlinear Physics of Complex Systems, vol. 476 of Lecture Notes in Physics, pp. 294–308. Springer, Berlin/Heidelberg (1996)

    Google Scholar 

  8. Benjamin R., Kawai R.: Inertial effects in Büttiker–Landauer motor and refrigerator at the overdamped limit. Phys. Rev. E 77, 051132 (2008)

    Article  ADS  Google Scholar 

  9. Izumida Y., Okuda K.: Onsager coefficients of a finite-time carnot cycle. Phys. Rev. E 80, 021121 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  10. Asfaw M., Bekele M.: Energetics of a simple microscopic heat engine. Phys. Rev. E 72, 056109 (2005)

    Article  ADS  Google Scholar 

  11. Bekele M., Rajesh S., Ananthakrishna G., Kumar N.: Effect of Landauer’s blow torch on the equilibration rate in a bistable potential. Phys. Rev. E 59, 143–149 (1999)

    Article  ADS  Google Scholar 

  12. Cecconi F., Diotallevi F., Marconi U.M.B., Puglisi A.: Fluid-like behavior of a one-dimensional granular gas. J. Chem. Phys. 120, 35 (2004)

    Article  ADS  Google Scholar 

  13. Cecconi F., Marconi U.M.B., Diotallevi F., Puglisi A.: Inelastic hard rods in a periodic potential. J. Chem. Phys. 121, 5125 (2004)

    Article  ADS  Google Scholar 

  14. Marconi U.M.B., Tarazona P.: Nonequilibrium inertial dynamics of colloidal systems. J. Chem. Phys. 124, 164901 (2006)

    Article  ADS  Google Scholar 

  15. Marconi U.M.B., Tarazona P., Cecconi F.: Theory of thermostatted inhomogeneous granular fluids: A self-consistent density functional description. J. Chem. Phys. 126, 164904 (2007)

    Article  ADS  Google Scholar 

  16. López C., Marconi U.M.B.: Multiple time-scale approach for a system of brownian particles in a nonuniform temperature field. Phys. Rev. E 75, 021101 (2007)

    Article  ADS  Google Scholar 

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Correspondence to Umberto Marini Bettolo Marconi.

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Cecconi, F., Costantini, G. & Marconi, U.M.B. Thermally induced directed currents in hard rod systems. Granular Matter 14, 111–114 (2012). https://doi.org/10.1007/s10035-012-0334-3

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