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.
REFERENCES
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).
D. Evans and D. Searles, Equilibrium microstates which generate the second law violating steady states, Phys. Rev. E 50:1645-1648 (1994).
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).
F. Bonetto, G. Gallavotti, and P. Garrido, Chaotic principle: An experimental test, Physica D 105:226-252 (1997).
F. Bonetto, N. Chernov, and J. Lebowitz, (Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium, Chaos 8:823-833 (1998).
S. Lepri, R. Livi, and P. Politi, Physica D 119:140 (1998).
D. Evans and D. Searles, The conjugate fluctuation theorem and Green-Kubo relations, preprint (1998), revised version in cond-mat#9902021.
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).
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.
G. Gallavotti, Reversible Anosov maps and large deviations, Mathematical Physics Electronic Journal, MPEJ, (http://mpej.unige.eh) 1:1-12 (1995).
J. L. Lebowitz, private communication.
G. Ayton and D. Evans, On the asymptotic convergence of the transient and steady state fluctuation theorems, cond-mat #9903409.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1004604804070