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Volumn 63, Issue 1, 2001, Pages

Heuristic derivation of continuum kinetic equations from microscopic dynamics

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EID: 18644372097     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.016102     Document Type: Article
Times cited : (9)

References (37)
  • 5
    • 85035267933 scopus 로고    scopus 로고
    • J. S. Langer, in Chance and Matter, edited by J. Souleti, J. Anninemus, and R. Stora, Les Houches XLVI, 1986 (Elsevier Science, Amsterdam, 1987)
    • J. S. Langer, in Chance and Matter, edited by J. Souleti, J. Anninemus, and R. Stora, Les Houches XLVI, 1986 (Elsevier Science, Amsterdam, 1987);
  • 8
  • 14
    • 85035301059 scopus 로고    scopus 로고
    • See e.g., D. J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena, 2nd ed. (World Scientific, Singapore, 1984)
    • See e.g., D. J. Amit, Field Theory, the Renormalization Group, and Critical Phenomena, 2nd ed. (World Scientific, Singapore, 1984).
  • 16
    • 85035288579 scopus 로고    scopus 로고
    • By “generic” we refer to systems that have nonzero probability current in configuration space [the terms enclosed by large parentheses in Eq. (A3)] even in stationary states. In the master equation, this corresponds to the breakdown of detailed balance, i.e., the right-hand side of Eq. (2) does not vanish term-by-term in stationary states but only after summation. Usually this is also accompanied by a breakdown of the fluctuation-dissipation theorem, and the lack of a well-defined free energy
    • By “generic” we refer to systems that have nonzero probability current in configuration space [the terms enclosed by large parentheses in Eq. (A3)] even in stationary states. In the master equation, this corresponds to the breakdown of detailed balance, i.e., the right-hand side of Eq. (2) does not vanish term-by-term in stationary states but only after summation. Usually this is also accompanied by a breakdown of the fluctuation-dissipation theorem, and the lack of a well-defined free energy.
  • 17
    • 85035282001 scopus 로고    scopus 로고
    • For critical properties, this is not a serious problem because the relevant physics is in the long-wavelength, long-time limits, where by virtue of universality, a kinetic equation postulated solely by symmetry considerations is sufficient. However, this often requires physical intuition and insight, whereas the present method does not
    • For critical properties, this is not a serious problem because the relevant physics is in the long-wavelength, long-time limits, where by virtue of universality, a kinetic equation postulated solely by symmetry considerations is sufficient. However, this often requires physical intuition and insight, whereas the present method does not.
  • 18
    • 0013402752 scopus 로고
    • Similar approaches exist in other contexts, such as in the surface growth problem, where the equation of motion for the surface profile may be derived by approximating the transtion rate by a power series in the slow variable (the height difference), followed by taking the continuum limit. See Z. Racz, M. Siegert, D. Liu, and M. Plischke, Phys. Rev. A 43, 5275 (1991).
    • (1991) Phys. Rev. A , vol.43 , pp. 5275
    • Racz, Z.1    Siegert, M.2    Liu, D.3    Plischke, M.4
  • 19
    • 85035268035 scopus 로고    scopus 로고
    • Due to factorizations, terms of (Formula presented) and higher are absent where n is the number of spins involved in the energetics in w of Eq. (2). For Glauber dynamics, (Formula presented)
    • Due to factorizations, terms of (Formula presented) and higher are absent where n is the number of spins involved in the energetics in w of Eq. (2). For Glauber dynamics, (Formula presented)
  • 24
  • 25
    • 0000234352 scopus 로고
    • B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1995), Vol. 17, and references therein
    • S. Katz, J. L. Lebowitz, and H. Spohn, Phys. Rev. B 28, 1655 (1983);B. Schmittmann and R. K. P. Zia, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1995), Vol. 17, and references therein.
    • (1983) Phys. Rev. B , vol.28 , pp. 1655
    • Katz, S.1    Lebowitz, J.L.2    Spohn, H.3
  • 34
    • 0009283604 scopus 로고    scopus 로고
    • G. Korniss, Ph.D. dissertation, Virginia Polytechnic Institute and State University, 1997 (unpublished)
    • G. Korniss and B. Schmittmann, Phys. Rev. E 56, 4072 (1997);G. Korniss, Ph.D. dissertation, Virginia Polytechnic Institute and State University, 1997 (unpublished).
    • (1997) Phys. Rev. E , vol.56 , pp. 4072
    • Korniss, G.1    Schmittmann, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.