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Volumn 193, Issue 1-4, 2004, Pages 53-66

On the (Boltzmann) entropy of non-equilibrium systems

Author keywords

Macroscopic evolution; Microscopic dynamics; Non equilibrium entropy; Phase space volume; Script H sign theorem

Indexed keywords

FUNCTIONS; GASES; MICROSCOPIC EXAMINATION; PHASE SPACE METHODS; STATISTICAL MECHANICS; THEOREM PROVING; THERMODYNAMIC STABILITY; THERMODYNAMICS;

EID: 2642553864     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.01.008     Document Type: Conference Paper
Times cited : (172)

References (38)
  • 3
    • 0004019889 scopus 로고
    • North-Holland, Amsterdam
    • For a historical survey see: S.G. Brush, The Kind of Motion We Call Heat, North-Holland, Amsterdam, 1976; M. Klein, The development of Boltzmann's statistical ideas, in: E.G.D. Cohen, W. Thirring (Eds.), The Boltzmann Equation, Acta Physica Austriaca Suppl. X, Vienna, 1973, p. 53.
    • (1976) The Kind of Motion We Call Heat
    • Brush, S.G.1
  • 4
    • 0346755999 scopus 로고
    • The development of Boltzmann's statistical ideas
    • E.G.D. Cohen, W. Thirring (Eds.), Vienna
    • For a historical survey see: S.G. Brush, The Kind of Motion We Call Heat, North-Holland, Amsterdam, 1976; M. Klein, The development of Boltzmann's statistical ideas, in: E.G.D. Cohen, W. Thirring (Eds.), The Boltzmann Equation, Acta Physica Austriaca Suppl. X, Vienna, 1973, p. 53.
    • (1973) The Boltzmann Equation, Acta Physica Austriaca Suppl. X , pp. 53
    • Klein, M.1
  • 5
    • 0002931947 scopus 로고
    • Pergamon, Elmsford, NY
    • (a) For a collection of basic papers from the second half of the nineteenth century on the subject (in English Trans.), see: S.G. Brush, Kinetic Theory, vols. 1 and 2, Pergamon, Elmsford, NY, 1965-1966; The apparently little known 1874 article by W. Thomson (Lord Kelvin), The kinetic theory of the dissipation of energy, Proceedings of the Royal Society of Edinburgh 8, 1874, pp. 325-328, reprinted there, is highly recommended;
    • (1965) Kinetic Theory , vol.1-2
    • Brush, S.G.1
  • 6
    • 0009366026 scopus 로고
    • The kinetic theory of the dissipation of energy
    • reprinted there, is highly recommended
    • (a) For a collection of basic papers from the second half of the nineteenth century on the subject (in English Trans.), see: S.G. Brush, Kinetic Theory, vols. 1 and 2, Pergamon, Elmsford, NY, 1965-1966; The apparently little known 1874 article by W. Thomson (Lord Kelvin), The kinetic theory of the dissipation of energy, Proceedings of the Royal Society of Edinburgh 8, 1874, pp. 325-328, reprinted there, is highly recommended;
    • (1874) Proceedings of the Royal Society of Edinburgh , vol.8 , pp. 325-328
    • Thomson, W.1
  • 7
    • 0003763756 scopus 로고
    • Barth, Leipzig
    • (b) L. Boltzmann, Vorlesungen über Gastheorie, 2 vols., Barth, Leipzig, 1896, 1898 (English Trans.: S.G. Brush, Lectures on Gas Theory, Cambridge University Press, London, 1964, reprinted Dover, 1995).
    • (1896) Vorlesungen über Gastheorie , vol.2
    • Boltzmann, L.1
  • 8
    • 0004205706 scopus 로고
    • English Trans., Cambridge University Press, London, 1964, reprinted Dover
    • (b) L. Boltzmann, Vorlesungen über Gastheorie, 2 vols., Barth, Leipzig, 1896, 1898 (English Trans.: S.G. Brush, Lectures on Gas Theory, Cambridge University Press, London, 1964, reprinted Dover, 1995).
    • (1995) Lectures on Gas Theory
    • Brush, S.G.1
  • 10
    • 5644232645 scopus 로고
    • Script H sign-theorem for the (modified) nonlinear Enskog equation
    • Resibois P. script H sign-theorem for the (modified) nonlinear Enskog equation J. Stat. Phys. 19:1978;593.
    • (1978) J. Stat. Phys. , vol.19 , pp. 593
    • Resibois, P.1
  • 11
    • 12044250952 scopus 로고
    • Boltzmann's entropy and time's arrow
    • (a) J.L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46 (1993) 32-38; Microscopic reversibility and macroscopic behavior: physical explanations and mathematical derivations, in: J.J. Brey, J. Marro, J.M. Rubí, M. San Miguel (Eds.), Proceedings of the Sitges Conference on 25 Years of Non-Equilibrium Statistical Mechanics, Barcelona, Spain, 1994, Lecture Notes in Physics, Springer-Verlag, Berlin, 1995; Microscopic origins of irreversible macroscopic behavior, Physica A 263 (1999) 516-527;
    • (1993) Phys. Today , vol.46 , pp. 32-38
    • Lebowitz, J.L.1
  • 12
    • 12044250952 scopus 로고
    • Microscopic reversibility and macroscopic behavior: Physical explanations and mathematical derivations
    • Barcelona, Spain
    • (a) J.L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46 (1993) 32-38; Microscopic reversibility and macroscopic behavior: physical explanations and mathematical derivations, in: J.J. Brey, J. Marro, J.M. Rubí, M. San Miguel (Eds.), Proceedings of the Sitges Conference on 25 Years of Non-Equilibrium Statistical Mechanics, Barcelona, Spain, 1994, Lecture Notes in Physics, Springer-Verlag, Berlin, 1995; Microscopic origins of irreversible macroscopic behavior, Physica A 263 (1999) 516-527;
    • (1994) Proceedings of the Sitges Conference on 25 Years of Non-Equilibrium Statistical Mechanics
    • Brey, J.J.1    Marro, J.2    Rubí, J.M.3    San Miguel, M.4
  • 13
    • 12044250952 scopus 로고
    • Springer-Verlag, Berlin
    • (a) J.L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46 (1993) 32-38; Microscopic reversibility and macroscopic behavior: physical explanations and mathematical derivations, in: J.J. Brey, J. Marro, J.M. Rubí, M. San Miguel (Eds.), Proceedings of the Sitges Conference on 25 Years of Non-Equilibrium Statistical Mechanics, Barcelona, Spain, 1994, Lecture Notes in Physics, Springer-Verlag, Berlin, 1995; Microscopic origins of irreversible macroscopic behavior, Physica A 263 (1999) 516-527;
    • (1995) Lecture Notes in Physics
  • 14
    • 0002542839 scopus 로고    scopus 로고
    • Microscopic origins of irreversible macroscopic behavior
    • (a) J.L. Lebowitz, Boltzmann's entropy and time's arrow, Phys. Today 46 (1993) 32-38; Microscopic reversibility and macroscopic behavior: physical explanations and mathematical derivations, in: J.J. Brey, J. Marro, J.M. Rubí, M. San Miguel (Eds.), Proceedings of the Sitges Conference on 25 Years of Non-Equilibrium Statistical Mechanics, Barcelona, Spain, 1994, Lecture Notes in Physics, Springer-Verlag, Berlin, 1995; Microscopic origins of irreversible macroscopic behavior, Physica A 263 (1999) 516-527;
    • (1999) Physica A , vol.263 , pp. 516-527
  • 15
    • 19144369709 scopus 로고    scopus 로고
    • Boltzmann's approach to statistical mechanics
    • J. Bricmont, et al. (Eds.), Springer-Verlag, Berlin. cond-mat/0105242
    • (b) S. Goldstein, Boltzmann's approach to statistical mechanics, in: J. Bricmont, et al. (Eds.), Chance in Physics: Foundations and Perspectives, Lecture Notes in Physics 574, Springer-Verlag, Berlin, 2001. cond-mat/0105242 .
    • (2001) Chance in Physics: Foundations and Perspectives, Lecture Notes in Physics , vol.574
    • Goldstein, S.1
  • 16
    • 0000830893 scopus 로고
    • The nature of the motion we call heat
    • reprinted in [4a]
    • R. Clausius, The nature of the motion we call heat, Ann. Phys. [2] 125 (1865) 353, reprinted in [4a].
    • (1865) Ann. Phys. [2] , vol.125 , pp. 353
    • Clausius, R.1
  • 17
    • 0242527943 scopus 로고
    • Thermodynamics and some molecular aspects of biology
    • G.C. Quarton, et al. (Eds.), Rockefeller University Press, New York
    • L. Onsager, Thermodynamics and some molecular aspects of biology, in: G.C. Quarton, et al. (Eds.), The Neurosciences: A Study Program, Rockefeller University Press, New York, 1967, pp. 75-79.
    • (1967) The Neurosciences: A Study Program , pp. 75-79
    • Onsager, L.1
  • 23
    • 26744448776 scopus 로고
    • O. Lanford, Time evolution of large classical systems, in: J. Moser (Ed.), Dynamical Systems, Theory and Applications, Lecture Notes in Physics 38, Springer-Verlag, Berlin, 1975; Physica A 106 (1981) 70.
    • (1981) Physica A , vol.106 , pp. 70
  • 24
    • 21344493381 scopus 로고    scopus 로고
    • Entropy production estimates for Boltzmann equation with physically realistic collision kernels
    • Carlen E., Carvalho M., Entropy production estimates for Boltzmann equation with physically realistic collision kernels. J. Stat. Phys. 74:1994;743-782 L. Desvillettes, C. Villani, On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation, Preprint.
    • (1994) J. Stat. Phys. , vol.74 , pp. 743-782
    • Carlen, E.1    Carvalho, M.2
  • 26
    • 0009447495 scopus 로고
    • Violation of Boltzmann's H theorem in real gases
    • Jaynes E.T., Violation of Boltzmann's H theorem in real gases. Phys. Rev. A. 4:1971;747-750.
    • (1971) Phys. Rev. A , vol.4 , pp. 747-750
    • Jaynes, E.T.1
  • 29
    • 0346672421 scopus 로고    scopus 로고
    • Time-reversal and entropy
    • Maes C., Netocny K., Time-reversal and entropy. J. Stat. Phys. 110:2003;269-310.
    • (2003) J. Stat. Phys. , vol.110 , pp. 269-310
    • Maes, C.1    Netocny, K.2
  • 30
    • 0006886326 scopus 로고    scopus 로고
    • Fourier's law: A challenge to theorists
    • A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (Eds.), Imperial College Press, London
    • F. Bonetto, J.L. Lebowitz, L. Rey-Bellet, Fourier's law: a challenge to theorists, in: A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (Eds.), Mathematical Physics 2000, Imperial College Press, London, 2000, pp. 128-150.
    • (2000) Mathematical Physics 2000 , pp. 128-150
    • Bonetto, F.1    Lebowitz, J.L.2    Rey-Bellet, L.3
  • 31
    • 4244208748 scopus 로고    scopus 로고
    • Dynamical ensembles in nonequilibrium statistical mechanics
    • Gallavotti G., Cohen E.G.D., Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 95(74):1995;2694 G. Gallavotti, Nonequilibrium thermodynamics, 2002, Preprint.
    • (1995) Phys. Rev. Lett. , vol.95 , Issue.74 , pp. 2694
    • Gallavotti, G.1    Cohen, E.G.D.2
  • 32
    • 4244208748 scopus 로고    scopus 로고
    • Preprint
    • Gallavotti G., Cohen E.G.D., Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 95(74):1995;2694 G. Gallavotti, Nonequilibrium thermodynamics, 2002, Preprint.
    • (2002) Nonequilibrium Thermodynamics
    • Gallavotti, G.1
  • 33
    • 0033246861 scopus 로고    scopus 로고
    • Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
    • Ruelle D., Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys. 95:1999;393-468 Extending the definition of entropy to nonequilibrium steady states, Proc. Natl. Acad. Sci. U.S.A. 100 (2003) 3054-3058. math phys archive 03-98 .
    • (1999) J. Stat. Phys. , vol.95 , pp. 393-468
    • Ruelle, D.1
  • 34
    • 0037453092 scopus 로고    scopus 로고
    • Extending the definition of entropy to nonequilibrium steady states
    • math phys archive 03-98
    • Ruelle D., Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys. 95:1999;393-468 Extending the definition of entropy to nonequilibrium steady states, Proc. Natl. Acad. Sci. U.S.A. 100 (2003) 3054-3058. math phys archive 03-98 .
    • (2003) Proc. Natl. Acad. Sci. U.S.A. , vol.100 , pp. 3054-3058
  • 35
    • 0031093453 scopus 로고    scopus 로고
    • Stationary nonequilibrium states in boundary driven Hamiltonian systems: Shear flow
    • cond-mat/9703097, Texas 97-113
    • N. Chernov, J.L. Lebowitz, Stationary nonequilibrium states in boundary driven Hamiltonian systems: shear flow, J. Stat. Phys. 86 (1997) 953-990. cond-mat/9703097, Texas 97-113.
    • (1997) J. Stat. Phys. , vol.86 , pp. 953-990
    • Chernov, N.1    Lebowitz, J.L.2
  • 36
    • 0004178218 scopus 로고
    • Lecture 14, Princeton University Press, Princeton, NJ
    • Ya.G. Sinai, Introduction to Ergodic Theory, Lecture 14, Princeton University Press, Princeton, NJ, 1976.
    • (1976) Introduction to Ergodic Theory
    • Sinai, Ya.G.1


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