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Volumn 16, Issue 2, 2004, Pages 281-315

Entropy production, information gain and Lyapunov exponents of random hyperbolic dynamical systems

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EID: 1042279091     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.2004.014     Document Type: Article
Times cited : (3)

References (50)
  • 1
    • 46549091018 scopus 로고
    • The rate of entropy change in non-Hamiltonian systems
    • Audrey L.: The rate of entropy change in non-Hamiltonian systems. Physics Letters 111A (1985), 45-46
    • (1985) Physics Letters , vol.111 A , pp. 45-46
    • Audrey, L.1
  • 3
    • 0002544333 scopus 로고
    • Entropy, pressure, and a variational principle for random dynamical systems
    • Bogenschütz T.: Entropy, pressure, and a variational principle for random dynamical systems. Random and Computational Dynamics 1 (1992), 99-116
    • (1992) Random and Computational Dynamics , vol.1 , pp. 99-116
    • Bogenschütz, T.1
  • 5
    • 85009367586 scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms
    • Springer-Verlag, Berlin
    • Bowen R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lec. Notes Math. 470. Springer-Verlag, Berlin 1975
    • (1975) Lec. Notes Math. , vol.470
    • Bowen, R.1
  • 6
    • 84974487290 scopus 로고
    • Ruelle's transfer operator for random subshifts of finite type
    • Bogenschütz T. and Gundlach V. M.: Ruelle's transfer operator for random subshifts of finite type. Ergod. Th. Dynam. Sys. 15 (1995), 413-447
    • (1995) Ergod. Th. Dynam. Sys. , vol.15 , pp. 413-447
    • Bogenschütz, T.1    Gundlach, V.M.2
  • 7
    • 54649083619 scopus 로고    scopus 로고
    • Characterization of measures satisfying Pesin's entropy formula for random dynamical systems
    • Bahnmüller J. and Liu P. D.: Characterization of measures satisfying Pesin's entropy formula for random dynamical systems. J. Dynam. Diff. Equa. 10 (1998), 425-448
    • (1998) J. Dynam. Diff. Equa. , vol.10 , pp. 425-448
    • Bahnmüller, J.1    Liu, P.D.2
  • 8
    • 84980178612 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time, I
    • Donsker M. D. and Varadhan S. R. S.: Asymptotic evaluation of certain Markov process expectations for large time, I. Comm. Pure Appl. Math. 28 (1975), 1-47; IV, Comm. Pure Appl. Math. 36 (1983), 183-212
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 1-47
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 9
    • 84990587390 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time IV
    • Donsker M. D. and Varadhan S. R. S.: Asymptotic evaluation of certain Markov process expectations for large time, I. Comm. Pure Appl. Math. 28 (1975), 1-47; IV, Comm. Pure Appl. Math. 36 (1983), 183-212
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 183-212
  • 10
    • 0000321213 scopus 로고
    • On entropy and information gain in random fields
    • Föllmer H.: On entropy and information gain in random fields. Z. Wahrsch. Verw. Gebiete 26 (1973), 207-217
    • (1973) Z. Wahrsch. Verw. Gebiete , vol.26 , pp. 207-217
    • Föllmer, H.1
  • 11
    • 0002810152 scopus 로고
    • Reversible Anosov diffeomorphisms and large deviations
    • Gallavotti G.: Reversible Anosov diffeomorphisms and large deviations. Math. Phys. Electronic J. 1 (1995), 1-12
    • (1995) Math. Phys. Electronic J. , vol.1 , pp. 1-12
    • Gallavotti, G.1
  • 12
    • 0030510671 scopus 로고    scopus 로고
    • Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
    • Gallavotti G.: Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem. J. Statist. Phys. 84 (1996), 899-926
    • (1996) J. Statist. Phys. , vol.84 , pp. 899-926
    • Gallavotti, G.1
  • 13
    • 0000642229 scopus 로고    scopus 로고
    • Extension of Onsager's reciprocity and fluctuation-dissipation theorem
    • Gallavotti G.: Extension of Onsager's reciprocity and fluctuation-dissipation theorem. Phys. Rev. Lett. 77 (1996), 4334-4337
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 4334-4337
    • Gallavotti, G.1
  • 14
    • 0001369553 scopus 로고    scopus 로고
    • Chaotic dynamics, fluctuations, nonequilibrium ensembles
    • Gallavotti G.: Chaotic dynamics, fluctuations, nonequilibrium ensembles. Chaos 8 (1998), 384-392
    • (1998) Chaos , vol.8 , pp. 384-392
    • Gallavotti, G.1
  • 15
    • 17044421499 scopus 로고
    • Dynamical ensembles in stationary states
    • Gallavotti G. and Cohen E. G. D.: Dynamical ensembles in stationary states. J. Statist. Phys. 80 (1995), 931-970
    • (1995) J. Statist. Phys. , vol.80 , pp. 931-970
    • Gallavotti, G.1    Cohen, E.G.D.2
  • 16
    • 0033164036 scopus 로고    scopus 로고
    • Entropy production: From open volume-preserving to dissipative systems
    • Gilbert T. and Dorfman J. R.: Entropy production: from open volume-preserving to dissipative systems. J. Statist. Phys. 96 (1999), 225-269
    • (1999) J. Statist. Phys. , vol.96 , pp. 225-269
    • Gilbert, T.1    Dorfman, J.R.2
  • 17
    • 0346411885 scopus 로고
    • The invariant measures, probability flow and circulations of one-dimensional Markov processes
    • Fukushima, M. (ed.) Functional analysis in Markov processes. Proceedings, Katata and Kyoto 1981. Berlin, Heidelberg: Springer-Verlag
    • Gong G. L. and Qian M. P.: The invariant measures, probability flow and circulations of one-dimensional Markov processes. In: Fukushima, M. (ed.) Functional analysis in Markov processes (Lec. Not. Math. 923). Proceedings, Katata and Kyoto 1981, pp. 188-198. Berlin, Heidelberg: Springer-Verlag 1982
    • (1982) Lec. Not. Math. , vol.923 , pp. 188-198
    • Gong, G.L.1    Qian, M.P.2
  • 20
    • 1042272944 scopus 로고    scopus 로고
    • Hasengawa H.: Progress of Theoretic Phys. Vol. 55, 90; Vol. 56, 44; Vol. 57, 1523; Vol. 58, 128
    • Progress of Theoretic Phys. , vol.56 , pp. 44
  • 21
    • 1042296177 scopus 로고    scopus 로고
    • Hasengawa H.: Progress of Theoretic Phys. Vol. 55, 90; Vol. 56, 44; Vol. 57, 1523; Vol. 58, 128
    • Progress of Theoretic Phys. , vol.57 , pp. 1523
  • 22
    • 1042296176 scopus 로고    scopus 로고
    • Hasengawa H.: Progress of Theoretic Phys. Vol. 55, 90; Vol. 56, 44; Vol. 57, 1523; Vol. 58, 128
    • Progress of Theoretic Phys. , vol.58 , pp. 128
  • 23
    • 0037001774 scopus 로고    scopus 로고
    • Lyapunov exponents of hyperbolic attractors
    • Jiang D. Q., Liu P. D. and Qian M.: Lyapunov exponents of hyperbolic attractors. Manuscripta Math. 108 (2002), 43-67
    • (2002) Manuscripta Math. , vol.108 , pp. 43-67
    • Jiang, D.Q.1    Liu, P.D.2    Qian, M.3
  • 24
    • 0034311689 scopus 로고    scopus 로고
    • Entropy production and information gain in Axiom-A systems
    • Jiang D. Q., Qian M. and Qian M. P.: Entropy production and information gain in Axiom-A systems. Commun. Math. Phys. 214 (2000), 389-409
    • (2000) Commun. Math. Phys. , vol.214 , pp. 389-409
    • Jiang, D.Q.1    Qian, M.2    Qian, M.P.3
  • 26
    • 51249166150 scopus 로고
    • Multidimensional random subshifts of finite type and their large deviations
    • Kifer Y.: Multidimensional random subshifts of finite type and their large deviations. Probab. Theory Relat. Fields 102 (1995), 223-248
    • (1995) Probab. Theory Relat. Fields , vol.102 , pp. 223-248
    • Kifer, Y.1
  • 27
    • 0003280184 scopus 로고
    • Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities
    • Springer-Verlag, Berlin
    • Katok A. and Strelcyn J. M.: Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities. Lec. Notes Math. 1222. Springer-Verlag, Berlin 1986
    • (1986) Lec. Notes Math. , vol.1222
    • Katok, A.1    Strelcyn, J.M.2
  • 28
    • 0033246864 scopus 로고    scopus 로고
    • A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics
    • Lebowitz J. L. and Spohn H.: A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics. J. Statist. Phys. 95 (1999), 333-365
    • (1999) J. Statist. Phys. , vol.95 , pp. 333-365
    • Lebowitz, J.L.1    Spohn, H.2
  • 29
    • 0031481078 scopus 로고    scopus 로고
    • Stability of orbit spaces of endomorphisms
    • Liu P. D.: Stability of orbit spaces of endomorphisms. Manuscripta Math. 93 (1997), 109-128
    • (1997) Manuscripta Math. , vol.93 , pp. 109-128
    • Liu, P.D.1
  • 30
    • 0031631675 scopus 로고    scopus 로고
    • Random perturbations of Axiom a basic sets
    • Liu P. D.: Random perturbations of Axiom A basic sets. J. Statist. Phys. 90 (1998), 467-490
    • (1998) J. Statist. Phys. , vol.90 , pp. 467-490
    • Liu, P.D.1
  • 31
    • 0003263856 scopus 로고
    • Smooth ergodic theory of random dynamical systems
    • Springer-Verlag, Berlin-Heidelberg
    • Liu P. D. and Qian M.: Smooth ergodic theory of random dynamical systems. Lec. Notes Math. 1606. Springer-Verlag, Berlin-Heidelberg 1995
    • (1995) Lec. Notes Math. , vol.1606
    • Liu, P.D.1    Qian, M.2
  • 32
    • 0033246860 scopus 로고    scopus 로고
    • The fluctuation theorem as a Gibbs property
    • Maes C.: The fluctuation theorem as a Gibbs property. J. Statist. Phys. 95 (1999), 367-392
    • (1999) J. Statist. Phys. , vol.95 , pp. 367-392
    • Maes, C.1
  • 33
    • 0034288242 scopus 로고    scopus 로고
    • Positivity of entropy production
    • Maes C. and Redig F.: Positivity of entropy production. J. Statist. Phys. 101 (2000), 315
    • (2000) J. Statist. Phys. , vol.101 , pp. 315
    • Maes, C.1    Redig, F.2
  • 34
    • 0034345461 scopus 로고    scopus 로고
    • On the definition of entropy production, via examples
    • Maes C., Redig F. and Moffaert A. V.: On the definition of entropy production, via examples. J. Math. Phys. 41 (2000), 1528-1554
    • (2000) J. Math. Phys. , vol.41 , pp. 1528-1554
    • Maes, C.1    Redig, F.2    Moffaert, A.V.3
  • 36
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems
    • Oseledec V. I.: A multiplicative ergodic theorem. Liapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968), 197-221
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-221
    • Oseledec, V.I.1
  • 37
    • 34250233688 scopus 로고
    • Circulation for recurrent Markov chains
    • Qian M. P. and Qian M.: Circulation for recurrent Markov chains. Z. Wahrsch. Verw. Gebiete 59 (1982), 203-210
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 203-210
    • Qian, M.P.1    Qian, M.2
  • 38
    • 0002598526 scopus 로고
    • The entropy production and reversibilty of Markov processes
    • Qian M. P. and Qian M.: The entropy production and reversibilty of Markov processes. Kexue Tongbao (China) 3 (1985), 165-167
    • (1985) Kexue Tongbao (China) , vol.3 , pp. 165-167
    • Qian, M.P.1    Qian, M.2
  • 39
    • 0009024944 scopus 로고
    • The entropy production and reversibilty of Markov processes
    • Prohorov, Yu. A. and Sazonov, V. V. (eds.) Probability theory and applications, Tashkent, USSR 1986. Utrecht: VNU Science Press
    • Qian M. P. and Qian M.: The entropy production and reversibilty of Markov processes. In: Prohorov, Yu. A. and Sazonov, V. V. (eds.) Probability theory and applications. Proceedings of the 1st World Congress of the Bernoulli Society, Tashkent, USSR 1986, pp. 307-316. Utrecht: VNU Science Press 1987
    • (1987) Proceedings of the 1st World Congress of the Bernoulli Society , pp. 307-316
    • Qian, M.P.1    Qian, M.2
  • 40
    • 0001503605 scopus 로고
    • The reversibility and the entropy production of Markov processes
    • Qian M. P., Qian M. and Gong G. L.: The reversibility and the entropy production of Markov processes. Contemp. Math. 118 (1991), 255-261
    • (1991) Contemp. Math. , vol.118 , pp. 255-261
    • Qian, M.P.1    Qian, M.2    Gong, G.L.3
  • 41
    • 0002391224 scopus 로고
    • Circulations of Markov chains with continuous time and the probability interpretation of some determinants
    • Qian M. P., Qian C. and Qian M.: Circulations of Markov chains with continuous time and the probability interpretation of some determinants. Sci. Sinica (Series A) 27 (1984), 470-481
    • (1984) Sci. Sinica (Series A) , vol.27 , pp. 470-481
    • Qian, M.P.1    Qian, C.2    Qian, M.3
  • 42
    • 0033425916 scopus 로고    scopus 로고
    • The entropy production of diffusion processes on manifolds and its circulation decopositions
    • Qian M. and Wang Z. D.: The entropy production of diffusion processes on manifolds and its circulation decopositions. Commun. Math. Phys. 206 (1999), 429-445
    • (1999) Commun. Math. Phys. , vol.206 , pp. 429-445
    • Qian, M.1    Wang, Z.D.2
  • 43
    • 0002802366 scopus 로고
    • On the fundamental ideas of measure theory
    • Rohlin V. A.: On the fundamental ideas of measure theory. Amer. Math. Soc. Transl. 10 (1962), 1-52
    • (1962) Amer. Math. Soc. Transl. , vol.10 , pp. 1-52
    • Rohlin, V.A.1
  • 44
    • 0004133384 scopus 로고
    • Addison Wesley Publishing Company, London
    • Ruelle D.: Thermodynamic Formalism. Addison Wesley Publishing Company, London 1978
    • (1978) Thermodynamic Formalism
    • Ruelle, D.1
  • 45
    • 51649166261 scopus 로고
    • Ergodic theory of differentiable dynamical systems
    • Ruelle D.: Ergodic theory of differentiable dynamical systems. Publ. Math. IHES 50 (1979), 275-306
    • (1979) Publ. Math. IHES , vol.50 , pp. 275-306
    • Ruelle, D.1
  • 46
    • 0030510906 scopus 로고    scopus 로고
    • Positivity of entropy production in nonequilibrium statistical mechanics
    • Ruelle D.: Positivity of entropy production in nonequilibrium statistical mechanics. J. Statist. Phys. 85 (1996), 1-23
    • (1996) J. Statist. Phys. , vol.85 , pp. 1-23
    • Ruelle, D.1
  • 47
    • 0031092587 scopus 로고    scopus 로고
    • Positivity of entropy production in the presence of a random thermostat
    • Ruelle D.: Positivity of entropy production in the presence of a random thermostat. J. Statist. Phys. 86 (1997), 935-951
    • (1997) J. Statist. Phys. , vol.86 , pp. 935-951
    • Ruelle, D.1
  • 48
    • 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. Statist. Phys. 95 (1999), 393-468
    • (1999) J. Statist. Phys. , vol.95 , pp. 393-468
    • Ruelle, D.1
  • 50
    • 0000013996 scopus 로고
    • Network theory of microscopic and macroscopic behaviour of master equation systems
    • Schnakenberg J.: Network theory of microscopic and macroscopic behaviour of master equation systems. Rev. Modern Phys. 48 (1976), 571-585
    • (1976) Rev. Modern Phys. , vol.48 , pp. 571-585
    • Schnakenberg, J.1


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