메뉴 건너뛰기




Volumn 152, Issue 3, 2013, Pages 569-597

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

Author keywords

Dynamical optimization; Model reduction; Nonequilibrium thermodynamics; Statistical closure

Indexed keywords


EID: 84880595754     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-013-0778-9     Document Type: Article
Times cited : (35)

References (48)
  • 1
    • 2442599290 scopus 로고    scopus 로고
    • Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation
    • Abramov, R., Kovacic, G., Majda, A. J.: Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation. Commun. Pure Appl. Math. 56, 1-46 (2003).
    • (2003) Commun. Pure Appl. Math. , vol.56 , pp. 1-46
    • Abramov, R.1    Kovacic, G.2    Majda, A.J.3
  • 4
    • 1442354885 scopus 로고    scopus 로고
    • Structure of equations of macrophysics
    • 066126
    • Berdichevsky, V. L.: Structure of equations of macrophysics. Phys. Rev. E 68, 066126 (2003).
    • (2003) Phys. Rev. E , vol.68
    • Berdichevsky, V.L.1
  • 8
    • 67650720543 scopus 로고    scopus 로고
    • Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
    • Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems. J. Stat. Phys. 135(5-6), 857-872 (2009).
    • (2009) J. Stat. Phys. , vol.135 , Issue.5-6 , pp. 857-872
    • Bertini, L.1    De Sole, A.2    Gabrielli, D.3    Jona-Lasinio, G.4    Landim, C.5
  • 12
    • 0034724367 scopus 로고    scopus 로고
    • Optimal prediction and the Mori-Zwanzig representation of irreversible processes
    • Chorin, A. J., Hald, O., Kupferman, R.: Optimal prediction and the Mori-Zwanzig representation of irreversible processes. Proc. Natl. Acad. Sci. USA 97, 2968-2973 (2000).
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 2968-2973
    • Chorin, A.J.1    Hald, O.2    Kupferman, R.3
  • 13
    • 0037097924 scopus 로고    scopus 로고
    • Optimal prediction with memory
    • Chorin, A. J., Hald, O., Kupferman, R.: Optimal prediction with memory. Physica D 166, 239-257 (2002).
    • (2002) Physica D , vol.166 , pp. 239-257
    • Chorin, A.J.1    Hald, O.2    Kupferman, R.3
  • 17
    • 0000333566 scopus 로고
    • Foundations of non-equilibrium statistical mechanics
    • Dougherty, J. P.: Foundations of non-equilibrium statistical mechanics. Philos. Trans. R. Soc. Lond. A 346, 259-305 (1994).
    • (1994) Philos. Trans. R. Soc. Lond. A , vol.346 , pp. 259-305
    • Dougherty, J.P.1
  • 20
    • 3042793188 scopus 로고    scopus 로고
    • Extracting macroscopic dynamics: model problems and algorithms
    • Givon, D., Kupferman, R., Stuart, A.: Extracting macroscopic dynamics: model problems and algorithms. Nonlinearity 17, 55-127 (2004).
    • (2004) Nonlinearity , vol.17 , pp. 55-127
    • Givon, D.1    Kupferman, R.2    Stuart, A.3
  • 22
    • 0001498447 scopus 로고
    • Particle and bracket formulations of kinetic theory
    • Grmela, M.: Particle and bracket formulations of kinetic theory. Contemp. Math. 28, 125-132 (1984).
    • (1984) Contemp. Math. , vol.28 , pp. 125-132
    • Grmela, M.1
  • 23
    • 0000313595 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. I. Development of a general formalism
    • Grmela, M., Öttinger, H. C.: Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620-6632 (1997).
    • (1997) Phys. Rev. E , vol.56 , pp. 6620-6632
    • Grmela, M.1    Öttinger, H.C.2
  • 24
    • 0002260533 scopus 로고
    • Where do we stand on maximum entropy
    • R. D. Levine and M. Tribus (Eds.), Cambridge: MIT Press
    • Jaynes, E. T.: Where do we stand on maximum entropy. In: Levine, R. D., Tribus, M. (eds.) The Maximum Entropy Formalism, pp. 15-118. MIT Press, Cambridge (1979).
    • (1979) The Maximum Entropy Formalism , pp. 15-118
    • Jaynes, E.T.1
  • 31
    • 0011685915 scopus 로고
    • A review of the matrix Riccati equation
    • Kučera, V.: A review of the matrix Riccati equation. Kybernetika 9, 42-61 (1973).
    • (1973) Kybernetika , vol.9 , pp. 42-61
    • Kučera, V.1
  • 35
    • 0033751055 scopus 로고    scopus 로고
    • Remarkable statistical behavior of truncated Burgers-Hopf dynamics
    • Majda, A. J., Timofeyev, I.: Remarkable statistical behavior of truncated Burgers-Hopf dynamics. Proc. Natl. Acad. Sci. USA 97, 12413-12417 (2000).
    • (2000) Proc. Natl. Acad. Sci. USA , vol.97 , pp. 12413-12417
    • Majda, A.J.1    Timofeyev, I.2
  • 36
    • 0002023117 scopus 로고    scopus 로고
    • Statistical mechanics for truncations of the Burgers-Hopf equation: a model for intrinsic stochastic behavior with scaling
    • Majda, A. J., Timofeyev, I.: Statistical mechanics for truncations of the Burgers-Hopf equation: a model for intrinsic stochastic behavior with scaling. Milan J. Math. 70, 39-96 (2002).
    • (2002) Milan J. Math. , vol.70 , pp. 39-96
    • Majda, A.J.1    Timofeyev, I.2
  • 37
    • 33645101025 scopus 로고    scopus 로고
    • Stochastic models for selected slow variables in large deterministic systems
    • Majda, A. J., Timofeyev, I., Vanden-Eijnden, E.: Stochastic models for selected slow variables in large deterministic systems. Nonlinearity 19, 769-794 (2006).
    • (2006) Nonlinearity , vol.19 , pp. 769-794
    • Majda, A.J.1    Timofeyev, I.2    Vanden-Eijnden, E.3
  • 38
    • 0001644158 scopus 로고
    • Bracket formulation for irreversible classical fields
    • Morrison, P. J.: Bracket formulation for irreversible classical fields. Phys. Lett. A 100, 423-427 (1984).
    • (1984) Phys. Lett. A , vol.100 , pp. 423-427
    • Morrison, P.J.1
  • 39
    • 0001637562 scopus 로고    scopus 로고
    • General projection operator formalism for the dynamics and thermodynamics of complex fluids
    • Öttinger, H. C.: General projection operator formalism for the dynamics and thermodynamics of complex fluids. Phys. Rev. E 57, 1416-1420 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 1416-1420
    • Öttinger, H.C.1
  • 41
    • 5344263088 scopus 로고    scopus 로고
    • Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism
    • Öttinger, H. C., Grmela, M.: Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys. Rev. E 56, 6633-6655 (1997).
    • (1997) Phys. Rev. E , vol.56 , pp. 6633-6655
    • Öttinger, H.C.1    Grmela, M.2
  • 42
    • 36149046859 scopus 로고
    • Foundations of statistical mechanics
    • Penrose, O.: Foundations of statistical mechanics. Rep. Prog. Phys. 42, 1937-2006 (1979).
    • (1979) Rep. Prog. Phys. , vol.42 , pp. 1937-2006
    • Penrose, O.1
  • 43
    • 0039616355 scopus 로고
    • Elementary derivation of nonlinear transport equations from statistical mechanics
    • Ramshaw, J. D.: Elementary derivation of nonlinear transport equations from statistical mechanics. J. Stat. Phys. 45, 983-999 (1986).
    • (1986) J. Stat. Phys. , vol.45 , pp. 983-999
    • Ramshaw, J.D.1
  • 44
    • 0002112643 scopus 로고
    • Application of maximum entropy to nonequilibrium statistical mechanics
    • R. D. Levine and M. Tribus (Eds.), Cambridge: MIT Press
    • Robertson, B.: Application of maximum entropy to nonequilibrium statistical mechanics. In: Levine, R. D., Tribus, M. (eds.) The Maximum Entropy Formalism, pp. 289-320. MIT Press, Cambridge (1979).
    • (1979) The Maximum Entropy Formalism , pp. 289-320
    • Robertson, B.1
  • 45
    • 0000035031 scopus 로고
    • Microscopic approach to irreversible thermodynamics, I: general theory
    • Vasconcellos, A. R., Luzzi, R., Garcia-Colin, L. S.: Microscopic approach to irreversible thermodynamics, I: general theory. Phys. Rev. A 43, 6622-6632 (1991).
    • (1991) Phys. Rev. A , vol.43 , pp. 6622-6632
    • Vasconcellos, A.R.1    Luzzi, R.2    Garcia-Colin, L.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.