The quantum-classical transition as an information flow

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Abstract

We investigate the classical limit of the semiclassical evolution with reference to a well-known model that represents the interaction between matter and a given field. This is done by recourse to a special statistical quantifier called the "symbolic transfer entropy". We encounter that the quantum-classical transition gets thereby described as the sign-reversal of the dominating direction of the information flow between classical and quantal variables. © 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland.

Figures

  • Figure 1. a) The directionality index T S vs. Er and b) T Sq,c and T Sc,q vs. Er, for a wide Er−range. We took q ≡ ⟨x2⟩ and c ≡ A. The classical variable A is dominant across most of the range, except for smallEr−values, for which Uncertainty Principle becomes important enough that the quantal variable ⟨x2⟩ becomes dominant. Note the absolute minimum of T S at Ercl = 21.55264, beginning of the transition region.
  • Figure 2. a) The directionality index T S vs. Er and b) T Sq,c and T Sc,q vs. Er, for an Er−range that allows to visualize the three zones of the process, i.e., quantal, transitional, and classic, delimited, respectively, by ErP = 3.3282, and Ercl = 21.55264. We took q ≡ ⟨x2⟩ and c ≡ A as in Figure 1. Note the absolute minimum of T S at Ercl, the local maximum at ErP , and the absolute maximum close by (Er ≃ 2.2). Symmetric information flow obtains at EMr = 6.81 (where the Statistical Complexity attains a maximum), well within the transition region. Classical variable A is the “leading” one from +∞ until this point. For smaller Er−values, ⟨x2⟩ becomes dominant.
  • Figure 3. The directionality index T S vs. Er and T Sq,c and T Sc,q vs. Er (inset). Here we took q ≡ ⟨x2⟩ and c ≡ PA. The three stages of the process are visible between ErP = 3.3282 and Er cl = 21.55264. Note the T S−absolute maximum at ErP . EMr is here slightly off the mark (see text).

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CITATION STYLE

APA

Kowalski, A. M., Martin, M. T., Zunino, L., Plastino, A., & Casas, M. (2010). The quantum-classical transition as an information flow. Entropy, 12(1), 148–160. https://doi.org/10.3390/e12010148

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