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No Current Without Heat

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Abstract

We show for a large class of interacting particle systems that whenever the stationary measure is not reversible for the dynamics, then the mean entropy production in the steady state is strictly positive. This extends to the thermodynamic limit the equivalence between microscopic reversibility and zero mean entropy production: time-reversal invariance cannot be spontaneously broken.

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REFERENCES

  1. J. L. Lebowitz and H. Spohn, A Gallavotti-Cohen type symmetry in the large deviation functional for stochastic dynamics, J. Stat. Phys. 95:333-365 (1999).

    Google Scholar 

  2. C. Maes, F. Redig, and M. Verschuere, Entropy production for interacting particle systems, Markov Proc. Rel. Fields 7:119-134 (2001).

    Google Scholar 

  3. C. Maes, The fluctuation theorem as a Gibbs property, J. Stat. Phys. 95:367-392(1999).

    Google Scholar 

  4. C. Maes, F. Redig, and A. Van Moffaert, On the definition of entropy production via examples, J. Math. Phys. 41:1528-1554 (2000).

    Google Scholar 

  5. C. Maes and F. Redig, Positivity of entropy production, J. Statist. Phys. 101:3-16 (2000).

    Google Scholar 

  6. C. Maes, Statistical Mechanics of Entropy Production: Gibbsian Hypothesis and Local Fluctuations, preprint from cond-mat/0106464.

  7. H. Künsch, Non reversible stationary measures for infinite interactingparticle systems, Z. Wahrsch. Verw. Gebiete 66:407 (1984).

    Google Scholar 

  8. T. M. Liggett, Interacting Particle Systems (Springer-Verlag, New York, Heidelberg, Berlin, 1985).

    Google Scholar 

  9. Z. Rieder, J. L. Lebowitz, and E. Lieb, Properties of a harmonic crystal in a stationary nonequilibrium state, J. Math. Phys. 8:1073-1078 (1967).

    Google Scholar 

  10. H. Nakazawa, On the lattice thermal conduction, Suppl. Prog. Theor. Phys. 45:231-262 (1970).

    Google Scholar 

  11. M. P. Qian, M. Qian, and C. Qian, Circulations of markov chains with continuous time and probability interpretation of some determinants, Sci. Sinica 27:470-481 (1984).

    Google Scholar 

  12. M. P. Qian and M. Qian, The Entropy Production and Reversibility of Markov Processes, Proceedings of the first world congress Bernoulli soc. (1988), pp. 307-316.

  13. J. Schnakenberg, Network theory of behavior of master equation systems, Rev. Mod. Phys. 48(4):571-585 (1976).

    Google Scholar 

  14. G. Gallavotti, Breakdown and regeneration of time reversal symmetry in nonequilibrium Statistical Mechanics, Physica D 112:250-257 (1998).

    Google Scholar 

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium

    Christian Maes & Michel Verschuere

  2. T.U. Eindhoven. On leave from Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium

    Frank Redig

Authors
  1. Christian Maes
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  2. Frank Redig
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  3. Michel Verschuere
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Maes, C., Redig, F. & Verschuere, M. No Current Without Heat. Journal of Statistical Physics 106, 569–587 (2002). https://doi.org/10.1023/A:1013706321846

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  • DOI: https://doi.org/10.1023/A:1013706321846

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