Mixing, entropy and competition

Klimenko, A. Y. (2012) Mixing, entropy and competition. Physica Scripta, 85 6: 068201.1-068201.29. doi:10.1088/0031-8949/85/06/068201

Author Klimenko, A. Y.
Title Mixing, entropy and competition
Journal name Physica Scripta   Check publisher's open access policy
ISSN 0031-8949
Publication date 2012-06
Year available 2012
Sub-type Article (original research)
DOI 10.1088/0031-8949/85/06/068201
Volume 85
Issue 6
Start page 068201.1
End page 068201.29
Total pages 29
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2013
Language eng
Formatted abstract
Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive systems and can be used to model a wide class of non-equilibrium phenomena ranging from turbulent premixed flames and invasion waves to complex competitive systems. We demonstrate consistency of the general principles of competition with thermodynamic description, review and analyse the related entropy concepts and introduce the corresponding competitive H-theorem. Acompetitive system can be characterized by a thermodynamic quantity - competitive potential - which determines the likely direction of evolution of the system. Contested resources tend to move between systems from lower to higher values of the competitive potential. There is, however, an important difference between conventional thermodynamics and competitive thermodynamics. While conventional thermodynamics is constrained by its zeroth law and is fundamentally transitive, the transitivity of competitive thermodynamics depends on the transitivity of the competition rules. Intransitivities are common in the real world and are responsible for complex behaviour in competitive systems. This work follows ideas and methods that have originated from the analysis of turbulent combustion, but reviews a much broader scope of issues linked to mixing and competition, including thermodynamic characterization of complex competitive systems with self-organization. The approach presented here is interdisciplinary and is addressed to the general educated readers, whereas the mathematical details can be found in the appendices.
Keyword Turbulent reactive flows
Probability density function
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mechanical & Mining Engineering Publications
Official 2013 Collection
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Citation counts: TR Web of Science Citation Count  Cited 8 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 8 times in Scopus Article | Citations
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Created: Wed, 10 Apr 2013, 14:03:01 EST by Karen Foster on behalf of School of Mechanical and Mining Engineering