Skip to main content
Log in

Note on Two Theorems in Nonequilibrium Statistical Mechanics

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

Abstract

An attempt is made to clarify the difference between a theorem derived by Evans and Searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state.

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.

REFERENCES

  1. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in non-equilibrium statistical mechanics, Phys. Rev. Lett. 74:2694-2697 (1995); G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in stationary states, J. Stat. Phys. 80:931-970 (1995).

    Google Scholar 

  2. D. Evans and D. Searles, Equilibrium microstates which generate the second law violating steady states, Phys. Rev. E 50:1645-1648 (1994).

    Google Scholar 

  3. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Probability of second law violations in shearing steady flows, Phys. Rev. Lett. 71:2401-2404 (1993).

    Google Scholar 

  4. F. Bonetto, G. Gallavotti, and P. Garrido, Chaotic principle: An experimental test, Physica D 105:226-252 (1997).

    Google Scholar 

  5. F. Bonetto, N. Chernov, and J. Lebowitz, (Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium, Chaos 8:823-833 (1998).

    Google Scholar 

  6. S. Lepri, R. Livi, and P. Politi, Physica D 119:140 (1998).

    Google Scholar 

  7. D. Evans and D. Searles, The conjugate fluctuation theorem and Green-Kubo relations, preprint (1998), revised version in cond-mat#9902021.

  8. Y. G. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys 27:21-69 (1972); and Lectures in Ergodic Theory, Lecture Notes in Mathematics (Princeton University Press, Princeton, 1977).

    Google Scholar 

  9. D. Ruelle, Smooth dynamics and new theoretical ideas in non-equilibrium statistical mechanics, Lecture notes, Rutgers University, mp_arc #98-770 (1998), or chao-dyn #9812032, in print on J. Stat. Phys.

  10. G. Gallavotti, Reversible Anosov maps and large deviations, Mathematical Physics Electronic Journal, MPEJ, (http://mpej.unige.eh) 1:1-12 (1995).

    Google Scholar 

  11. J. L. Lebowitz, private communication.

  12. G. Ayton and D. Evans, On the asymptotic convergence of the transient and steady state fluctuation theorems, cond-mat #9903409.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cohen, E.G.D., Gallavotti, G. Note on Two Theorems in Nonequilibrium Statistical Mechanics. Journal of Statistical Physics 96, 1343–1349 (1999). https://doi.org/10.1023/A:1004604804070

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004604804070

Navigation