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Shannon entropy, Fisher information and uncertainty relations for log-periodic oscillators

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  • Aguiar, V.
  • Guedes, I.

Abstract

We calculate the time-dependent Shannon (Sx and Sp) entropy and Fisher (Fx and Fp) information of three log-periodic oscillators. We obtain a general expression for Sx,p and Fx,p in the state n=0 in terms of ρ, a c-number quantity satisfying a nonlinear differential equation. For two out of three oscillators Sx,p and Fx,p depend on time, but Sx+Sp and FxFp do not. The other oscillator behaves as the time-independent harmonic oscillator where Sx,p and Fx,p are all constants. Relations among the Fisher information and the Stam and Cramer–Rao inequalities are also discussed.

Suggested Citation

  • Aguiar, V. & Guedes, I., 2015. "Shannon entropy, Fisher information and uncertainty relations for log-periodic oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 72-79.
    • Handle: RePEc:eee:phsmap:v:423:y:2015:i:c:p:72-79
    DOI: 10.1016/j.physa.2014.12.031
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    Cited by:

    1. Rui Miao & Xiaohao Xiang & Qi Wu & Zhibin Jiang, 2020. "Evaluation method of medical service system based on DEMATEL and the information entropy: A case study of hypertension diagnosis and treatment in China," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-15, December.

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