Complementarity in Classical Dynamical Systems

被引：0
作者：
Peter beim Graben
Harald Atmanspacher
机构：
[1] Universität Potsdam,Institut für Linguistik and Institut für Physik
[2] Institut für Grenzgebiete der Psychologie und Psychohygiene,undefined
[3] Parmenides Foundation,undefined
来源：
Foundations of Physics | 2006年 / 36卷
关键词：
algebraic system theory; complementarity; dynamical systems; symbolic dynamics; epistemic accessibility; generating partitions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.
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页码：291 / 306
页数：15
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共 72 条
  • [1] Adler R.L.(1967)“Entropy, a complete metric invariant for automorphisms of the torus” Proc. Natl. Acad. Sci. U.S.A. 57 1573-1576
  • [2] Weiss B.(1992)“A ‘quantal’ Hilbert space formulation for nonlinear dynamical systems in terms of probability amplitudes” Phys. Lett. A 163 41-43
  • [3] Alanson T.(1996)“An algebraic approach to the Kolmogorov-Sinai entropy” Rev. Math. Phys. 8 167-184
  • [4] Alicki R.(1993)“Generalized spectral decomposition of mixing dynamical systems” Int. J. Quant. Chem. 46 425-474
  • [5] Andries J.(2002)“Weak quantum theory: Complementarity and entanglement in physics and beyond” Found. Phys. 32 379-406
  • [6] Fannes M.(1987)“A fundamental link between system theory and statistical mechanics” Found. Phys. 17 939-963
  • [7] Tuyls P.(2004)“Incompatible implementations of physical symbol systems” Mind Matter 2 29-51
  • [8] Antoniou I.(2000)“Symbolic dynamics of event–related brain potentials” Phys. Rev. E 62 5518-5541
  • [9] Tasaki S.(1932)“Chemistry and the quantum theory of atomic constitution” J. Chem. Soc. 134 349-384
  • [10] Atmanspacher H.(2000)“Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series” Phys. Rev. Lett. 85 3524-3527
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