Trajectory versus probability density entropy

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In this article, the authors show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable.

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9 p.

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Bologna, Mauro; Grigolini, Paolo; Karagiorgis, Markos & Rosa, Angelo 2001.

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In this article, the authors show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable.

Physical Description

9 p.

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Copyright 2001 American Physical Society. The following article appeared in Physical Review E, 64:1; http://pre.aps.org/abstract/PRE/v64/i1/e016223

Abstract: We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.

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  • Physical Review E, 2001, College Park: American Physical Society

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  • Publication Title: Physical Review E
  • Volume: 64
  • Issue: 1
  • Pages: 9
  • Peer Reviewed: Yes

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UNT Scholarly Works

The Scholarly Works Collection is home to materials from the University of North Texas community's research, creative, and scholarly activities and serves as UNT's Open Access Repository. It brings together articles, papers, artwork, music, research data, reports, presentations, and other scholarly and creative products representing the expertise in our university community.** Access to some items in this collection may be restricted.**

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  • 2001

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  • March 9, 2012, 2:17 p.m.

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  • April 1, 2014, 12:26 p.m.

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Bologna, Mauro; Grigolini, Paolo; Karagiorgis, Markos & Rosa, Angelo. Trajectory versus probability density entropy, article, 2001; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc77165/: accessed February 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.