Trajectory versus probability density entropy

Description:

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.

Creator(s):
Creation Date: 2001  
Partner(s):
UNT College of Arts and Sciences
Collection(s):
UNT Scholarly Works
Usage:
Total Uses: 71
Past 30 days: 2
Yesterday: 0
Creator (Author):
Bologna, Mauro

University of North Texas

Creator (Author):
Grigolini, Paolo

University of North Texas; Istituto di Biofisica CNR; Universit√° di Pisa

Creator (Author):
Karagiorgis, Markos

University of North Texas

Creator (Author):
Rosa, Angelo

Istituto di Biofisica CNR

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
Date(s):
  • Creation: 2001
Description:

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.

Degree:
Department: Physics
Note:

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

Note:

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.

Physical Description:

9 p.

Language(s):
Subject(s):
Keyword(s): density entropy | transport equations
Source: Physical Review E, 2001, College Park: American Physical Society
Partner:
UNT College of Arts and Sciences
Collection:
UNT Scholarly Works
Identifier:
  • DOI: 10.1103/PhysRevE.64.016223
  • ARK: ark:/67531/metadc77165
Resource Type: Article
Format: Text
Rights:
Access: Public
Citation:
Publication Title: Physical Review E
Volume: 64
Issue: 1
Pages: 9
Peer Reviewed: Yes