Skip to main content
Log in

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

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

Abstract

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. Bernardin and S. Olla, Fourier’s law for a microscopic model of heat conduction. J. Stat. Phys. 121(3–4):271–289 (2005).

    Article  MATH  Google Scholar 

  2. J. Bricmont and A. Kupaianen, On the derivation of Fourier’s law for coupled anharmonic oscillators, arXiv:math-ph/0605062v1.

  3. F. Bonetto, J. L. Lebowitz, and L. Rey-Bellet, Fourier’s Law: a challenge to theorists. Math. Phys. 2000 (London Imp. Coll. Press, 2000), pp. 128–150.

  4. J.-P. Eckmann and L.-S. Young, Temperature profiles in Hamiltonian heat conduction. Europhys. Lett. 68:790–796 (2004).

    Article  ADS  Google Scholar 

  5. J.-P. Eckmann and L.-S. Young, Nonequilibrium energy profiles for a class of 1-D models. Commun. Math. Phys. 262:237–267 (2006).

    Article  MATH  ADS  Google Scholar 

  6. G. Eyink, J. Lebowitz, and H. Spohn, Hydrodynamics of stationary nonequilibrium states for some stochastic lattice gas models. Commun. Math. Phys. 132:253–283 (1990).

    Article  MATH  ADS  Google Scholar 

  7. S. de Groot and P. Mazur, Nonequilibrium Thermodynamics, North Holland (1962).

  8. C. Knipnis, C. Marchioro, and E. Presutti, Heat flow in an exactly solvable model. J. Stat. Phys. 27:65–74 (1982).

    Article  Google Scholar 

  9. H. Larralde, F. Leyvraz, and C. Mejia-Monasterio, Transport properties of a modified Lorentz gas. J. Stat. Phys. 113:197–231 (2003).

    Article  MATH  Google Scholar 

  10. J. Lebowitz, E. Presutti, and H. Spohn, Microscopic models of hydrodynamic behavior. J. Stat. Phys. 51(5/6):841–862 (1988).

    Article  MATH  Google Scholar 

  11. S. Lepri, R. Levi, and A. Politi, Thermal conduction in classical low-dimensional lattices. Phys. Rep. 377:1–80 (2003).

    Article  ADS  Google Scholar 

  12. A. de Masi and E. Presutti, Mathematical methods for hydrodynamic limits, Lecture Notes of Mathematics, Springer, vol. 1501: (1991).

  13. C. Mejia-Monasterio, H. Larralde, and F. Leyvraz, Coupled normal heat and matter transport in a simple model system. Phys. Rev. Lett. 86:5417–5420 (2001).

    Article  ADS  Google Scholar 

  14. K. Rateitschak, R. Klages, and G. Nicolis, Thermostating by deterministic scattering: the periodic Lorentz gas. J. Stat. Phys. 99:1339–1364 (2000).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Ravishankar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ravishankar, K., Young, LS. Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin. J Stat Phys 128, 641–665 (2007). https://doi.org/10.1007/s10955-007-9335-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-007-9335-8

Keywords

Navigation