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On the Convergence of Entropy for Stationary Exclusion Processes with Open Boundaries

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Abstract

We prove that, for a wide class of stochastic lattice gases in contact with reservoirs, despite long-range correlations, the leading-order term of the Gibbs–Shannon entropy in the nonequilibrium stationary state is given by the local equilibrium entropy.

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References

  1. C. Bahadoran, Hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries. Preprint.

  2. L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctuation theory for stationary nonequilibrium states. J. Stat. Phys. 107:635–675 (2002).

    Article  MATH  Google Scholar 

  3. C. Bardos and A. Y. Leroux, J. C. Nédélec, First order quasilinear equations with boundary conditions. Comm. Partial Differential Equations 4:1017–1034 (1979).

    MATH  MathSciNet  Google Scholar 

  4. B. Derrida and C. Enaud, Large deviation functional of the weakly asymmetric exclusion process. J. Stat. Phys. 114:537–562 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Derrida, M. Evans, V. Hakim and V. Pasquier, Exact solution of a ID asymmetric exclusion model using a matrix formulation. J. Phys. A 1493–1517 (1993).

  6. B. Derrida, C. Enaud and J. L. Lebowitz, The asymmetric exclusion process and brownian excursions. J. Stat. Phys. 115:365–383 (2004).

    Article  MathSciNet  Google Scholar 

  7. B. Derrida, C. Enaud, C. Landim and S. Olla, Fluctuations in the weakly asymmetric exclusion process with open boundary conditions. J. Stat. Phys. 118:795–811 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Derrida, J. L. Lebowitz and E. R. Speer, Large deviation of the density profile in the symmetric simple exclusion process. J. Stat. Phys. 107:599–634 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Derrida, J. L. Lebowitz and E. R. Speer, Exact large deviation functional of a stationary open driven diffusive system: The asymmetric exclusion process. J. Stat. Phys. 110:775–810 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  10. B. Derrida, J. L. Lebowitz and E. Speer, Entropy of open lattice systems. Preprint, to appear in J. Stat. Phys.

  11. R. Ellis, Entropy, large deviations and statistical mechanics. Grun-delhren der matematischen Wissenschaften, vol. 271 (Springer Verlag).

  12. G. Eyink, J. Lebowitz and H. Spohn, Hydrodynamics of stationary non-equilibrium states for some stochastic lattics gas models. Commun. Math. Phys. 132:253–283 (1990).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. G. Eyink, J. Lebowitz and H. Spohn, Lattice gas models in contact with stochastic reservoirs: local equilibrium and relaxation to the steady state. Comm. Math. Phys. 140:119–131 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. C. Kipnis and C. Landim, Scaling limits of infinite particle systems. (Springer, 1999).

  15. C. Kipnis, C. Landim and S. Olla, Macroscopic properties of a stationary non-equilibrium dsitribution for a non-gradient interacting particle system. Ann. Inst. H. Poincaré 31:191–221 (1995).

    MATH  MathSciNet  Google Scholar 

  16. E. Kosygina, The behavior of the specific entropy in the hydrodynamic scaling limit. Ann. Probab. (2000).

  17. T. Liggett, Ergodic theorems for the asymmetric simple exclusion process II. Ann. Probab. 5:795–801 (1977).

    MATH  MathSciNet  Google Scholar 

  18. V. Popkov and G. Schütz, Steady state selection in driven diffusive systems with open boundaries. Europhys. Lett. 48:257–263 (1999).

    Article  ADS  Google Scholar 

  19. F. Rezakhanlou, Hydrodynamic limit for attractive particle systems on Z d. Commun. Math. Phys. 140:417–448 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. D. Serre, Systems of conservation laws. Translated from the 1996 French original by I. N. Sneddon (Cambridge University Press, Cambridge).

  21. H. Spohn, Long-range correlations for stochastic lattice gases in a non-equilibrium steady state. J. Phys. A 16:4275–4291 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  22. H. Spohn, Large scale dynamics of interacting particles. Springer series, texts and monographs in Physics (1990).

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Bahadoran, C. On the Convergence of Entropy for Stationary Exclusion Processes with Open Boundaries. J Stat Phys 126, 1069–1082 (2007). https://doi.org/10.1007/s10955-006-9229-1

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