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Communications in Mathematical Physics (297)
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Chernov, N. I., Eyink, G. L., Lebowitz, J. L., & Sinai, Ya. G. (1993). Steady-state electrical conduction in the periodic Lorentz gas. Communications in Mathematical Physics, 154(3), 569–601.

Authors 4
  1. N. I. Chernov (first)
  2. G. L. Eyink (additional)
  3. J. L. Lebowitz (additional)
  4. Ya. G. Sinai (additional)
References 46 Referenced 171
  1. Abramov, L.M.: On the Entropy of a Flow. Dokl. Akad. Nauk SSSR128, 873–875 (1959) / Dokl. Akad. Nauk SSSR by L.M. Abramov (1959)
  2. Bunimovich, L.A., Sinai, Ya.G.: Markov Partitions for Dispersed Billiards. Commun. Math. Phys.73, 247–280 (1980) (10.1007/BF01942372) / Commun. Math. Phys. by L.A. Bunimovich (1980)
  3. Bunimovich, L.A., Sinai, Ya.G.: Statistical Properties of Lorentz Gas with Periodic Configuration of Scatterers. Commun. Math. Phys.78, 479–497 (1981) (10.1007/BF02046760) / Commun. Math. Phys. by L.A. Bunimovich (1981)
  4. Bunimovich, L.A., Sinai, Ya.G., Chernov, N.I.: Markov Partitions for Two-Dimensional Hyperbolic Billiards. Russ. Math. Surv.45, 105–152 (1990) (10.1070/RM1990v045n03ABEH002355) / Russ. Math. Surv. by L.A. Bunimovich (1990)
  5. Bunimovich, L.A., Sinai, Ya.G., Chernov, N.I.: Statistical Properties of Two-Dimensional Hyperbolic Billiards. Russ. Math. Surv.46, 47–106 (1991) (10.1070/RM1991v046n04ABEH002827) / Russ. Math. Surv. by L.A. Bunimovich (1991)
  6. Bunimovich, L.A.: A Theorem on Ergodicity of Two-Dimensional Hyperbolic Billiards. Commun. Math. Phys.130, 599–621 (1990) (10.1007/BF02096936) / Commun. Math. Phys. by L.A. Bunimovich (1990)
  7. Chernov, N.I.: The Ergodicity of a Hamiltonian System of Two Particles in an External Field. Physica D53, 233–239 (1991) (10.1016/0167-2789(91)90063-F) / Physica D by N.I. Chernov (1991)
  8. Chernov, N.I.: Ergodic and Statistical Properties of Piecewise Linear Hyperbolic Automorphisms of the 2-Tours. J. Stat. Phys.69, 111–134 (1992) (10.1007/BF01053785) / J. Stat. Phys. by N.I. Chernov (1992)
  9. Chernov, N.I.: Statistical Properties of the Periodic Lorentz Gas: Multidimensional Case. In preparation
  10. Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic Theory. Berlin, Heidelberg, New York: Springer 1982 (10.1007/978-1-4615-6927-5) / Ergodic Theory by I.P. Cornfeld (1982)
  11. Donnay, V., Liverani, C.: Potentials on the Two-Torus for Which the Hamiltonian Flow is Ergodic. Commun. Math. Phys.135, 267–302 (1991) (10.1007/BF02098044) / Commun. Math. Phys. by V. Donnay (1991)
  12. Evans, D.J., Morriss, G.P.: Statistical Mechanics of Nonequilibrium Liquids. San Diego, CA: Academic Press 1990 / Statistical Mechanics of Nonequilibrium Liquids by D.J. Evans (1990)
  13. Eyink, G.L., Lebowit, J.L., Spohn, H.: Microscopic Origin of Hydrodynamic Behavior: Entropy Production and the Steady State. Chaos/Xaoc Soviet-American Perspectives on Nonlinear Science. New York: American Institute of Physics, 1990, pp. 367–391 / Microscopic Origin of Hydrodynamic Behavior: Entropy Production and the Steady State. Chaos/Xaoc Soviet-American Perspectives on Nonlinear Science by G.L. Eyink (1990)
  14. Eyink, G.L., Lebowitz, J.L., Spohn, H.: Hydrodynamics of Stationary Non-Equilibrium States for Some Stochastic Lattice Gas Models. Commun. Math. Phys.132, 253–283 (1990) (10.1007/BF02278011) / Commun. Math. Phys. by G.L. Eyink (1990)
  15. Gallavotti, G., Ornstein, D.: Billiards and Bernoulli schemes. Commun. Math. Phys.38, 83–101 (1974) (10.1007/BF01651505) / Commun. Math. Phys. by G. Gallavotti (1974)
  16. Gauss, K.F.: Uber ein neues allgemeines Grundgesetz der Mechanik. J. Reine Angew. Math.IV, 232–235 (1829) (10.1515/crll.1829.4.232) / J. Reine Angew. Math. by K.F. Gauss (1829)
  17. Goldstein, S., Kipnis, C., Ianiro, N.: Stationary States for a Mechanical System with Stochastic Boundary Conditions. J. Stat. Phys.41, 915–939 (1985) (10.1007/BF01010010) / J. Stat. Phys. by S. Goldstein (1985)
  18. Goldstein, S., Lebowitz, J.L., Presutti, E.: Mechanical Systems with Stochastic Boundaries. Colloquia Mathematicae Societatis Janos Bolyai27, Random Fields. Amsterdam: North-Holland 1981 / Mechanical Systems with Stochastic Boundaries / 27, Random Fields by S. Goldstein (1981)
  19. de Groot, S., Masur, P.: Nonequilibrium Thermodynamics. Amsterdam: North-Holland 1962 / Nonequilibrium Thermodynamics by S. Groot de (1962)
  20. Hoover, W.G.: Computational Statistical Mechanics. Amsterdam; Elsevier 1991 / Computational Statistical Mechanics by W.G. Hoover (1991)
  21. Ibragimov, I.A., Linnik, Y.V.: Independent and Stationary Sequences of Random Variables. Gröningen: Wolters-Noordhoff 1971 / Independent and Stationary Sequences of Random Variables by I.A. Ibragimov (1971)
  22. van Kampen, N.: The Case Against Linear Response Theory. Physica Norvegica5, 279–284 (1971) / Physica Norvegica by N. Kampen van (1971)
  23. Katok, A., Strelcyn, J.-M.: Invariant Manifolds, Entropy, and Billiards; Smooth Maps with Singularities. Lecture Notes in Mathematics, vol.1222, New York: Springer 1986 (10.1007/BFb0099031) / Invariant Manifolds, Entropy, and Billiards; Smooth Maps with Singularities / Lecture Notes in Mathematics by A. Katok (1986)
  24. Katz, S., Lebowitz, J.L., Spohn, H.: Nonequilibrium Steady States of Stochastic Lattice Gas Models of Fast Ionic Conductors. J. Stat. Phys.34, 497–537 (1984) (10.1007/BF01018556) / J. Stat. Phys. by S. Katz (1984)
  25. Krámli, A., Simányi, N., Száss, D.: A “Transversal” Fundamental Theorem for Semi-Dispersing Billiards. Commun. Math. Phys.129, 535–560 (1990) (10.1007/BF02097105) / Commun. Math. Phys. by A. Krámli (1990)
  26. Kubo, R.: Statistical Mechanical Theory of Irreversible Processes. I. J. Phys. Soc. Jap.12, 570–586 (1957) (10.1143/JPSJ.12.570) / J. Phys. Soc. Jap. by R. Kubo (1957)
  27. Lebowitz, J.L.: Stationary Nonequilibrium Gibbsian Ensembles. Phys. Rev.114, 1192–1202 (1959) (10.1103/PhysRev.114.1192) / Phys. Rev. by J.L. Lebowitz (1959)
  28. Lebowitz, J.L., Bergmann, P.G.: Irreversible Gibbsian Ensembles. Ann. Phys.1, 1–23 (1957) (10.1016/0003-4916(57)90002-7) / Ann. Phys. by J.L. Lebowitz (1957)
  29. McLennan, J.A. Jr.: Statistical Mechanics of the Steady State. Phys. Rev.115, 1405–1409 (1959) (10.1103/PhysRev.115.1405) / Phys. Rev. by J.A. McLennan Jr. (1959)
  30. Moran, B., Hoover, W.: Diffusion in a Periodic Lorentz Gas. J. Stat. Phys.48, 709–726 (1987) (10.1007/BF01019693) / J. Stat. Phys. by B. Moran (1987)
  31. Morris, G.P., Evans, D.J., Cohen, E.G.D., van Beijeren, H.: Phys. Rev. Lett.62, 1579 (1989) (10.1103/PhysRevLett.62.1579) / Phys. Rev. Lett. by G.P. Morris (1989)
  32. Ornstein, D.S., Weiss, B.: Statistical Properties of Chaotic Systems. Bull. Am. Math. Soc.24, 11–116 (1991) (10.1090/S0273-0979-1991-15953-7) / Bull. Am. Math. Soc. by D.S. Ornstein (1991)
  33. Ruelle, D.: Thermodynamic Formalism. New York: Addison-Wesley 1978 / Thermodynamic Formalism by D. Ruelle (1978)
  34. Sinai, Ya.G.: Dynamical Systems with Elastic Reflections. Ergodic Properties of Dispersing Billiards. Russ. Math. Surv.25, 137–189 (1970) (10.1070/RM1970v025n02ABEH003794) / Math. Surv. by Ya.G. Sinai (1970)
  35. Sinai, Ya.G., Chernov, N.I.: Ergodic Properties of some Systems of 2-Dimensional Discs and 3-Dimensional Spheres. Russ. Math. Surv.42, 181–207 (1987) (10.1070/RM1987v042n03ABEH001421) / Russ. Math. Surv. by Ya.G. Sinai (1987)
  36. Sinai, Ya.G.: Hyperbolic Billiards. Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990
  37. Toda, M., Kubo, R., Hashitume, N.: Statistical Physics II. Non-equilibrium Statistical Mechanics. Berlin, Heidelberg, New York: Springer 1985 / Statistical Physics II. Non-equilibrium Statistical Mechanics by M. Toda (1985)
  38. Vaienti, S.: Ergodic Properties of the Discontinuous Sawtooth Map. J. Statist. Phys.67 (1992) (to appear) (10.1007/BF01049033)
  39. Vul, E.B., Sinai, Ya.G., Khanin, K.M.: Feigenbaum Universality and Thermodynamic Formalism. Russ. Math. Surv.39, 1–40 (1984) (10.1070/RM1984v039n03ABEH003162) / Russ. Math. Surv. by E.B. Vul (1984)
  40. Wojtkowski, M.: Principles for the Design of Billiards with Nonvanishing Lyapunov Exponents. Commun. Math. Phys.105, 391–414 (1986) (10.1007/BF01205934) / Commun. Math. Phys. by M. Wojtkowski (1986)
  41. Yamada, T., Kawasaki, K.: Nonlinear Effects in the Shear Viscosity of a Critical Mixture. Prog. Theor. Phys.38, 1031–1051 (1967) (10.1143/PTP.38.1031) / Prog. Theor. Phys. by T. Yamada (1967)
  42. Young L.-S.: Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps. Trans. Am. Math. Soc.281, 41–48 (1985) (10.1090/S0002-9947-1985-0766205-1) / Trans. Am. Math. Soc. by L.-S. Young (1985)
  43. Young, L.-S.: Dimension, Entropy and Lyapunov Exponents. Erg. Th. and Dyn. Syst.2, 109–124 (1982) (10.1017/S0143385700009615) / Erg. Th. and Dyn. Syst. by L.-S. Young (1982)
  44. Zubarev, D.N.: The Statistical Operator for Nonequilibrium Systems. Sov. Phys. Dokl.6, 776–778 (1962) / Sov. Phys. Dokl. by D.N. Zubarev (1962)
  45. Zubarev, D.N.: Nonequilibrium Statistical Thermodynamics. New York: Consultants 1974. / Nonequilibrium Statistical Thermodynamics by D.N. Zubarev (1974)
  46. Chernov, N.I., Eyink, G.L., Lebowitz, J.L., Sinai, Ya.G., Derivation of Ohm's Law in a Deterministic Mechanical Model. Submitted to Phys. Ref. Let.
Dates
Type When
Created 19 years, 9 months ago (Oct. 28, 2005, 9:16 p.m.)
Deposited 6 years, 3 months ago (May 13, 2019, 4:51 p.m.)
Indexed 2 weeks, 1 day ago (Aug. 6, 2025, 8:50 a.m.)
Issued 32 years, 2 months ago (June 1, 1993)
Published 32 years, 2 months ago (June 1, 1993)
Published Print 32 years, 2 months ago (June 1, 1993)
Funders 0

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@article{Chernov_1993, title={Steady-state electrical conduction in the periodic Lorentz gas}, volume={154}, ISSN={1432-0916}, url={http://dx.doi.org/10.1007/bf02102109}, DOI={10.1007/bf02102109}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Chernov, N. I. and Eyink, G. L. and Lebowitz, J. L. and Sinai, Ya. G.}, year={1993}, month=jun, pages={569–601} }