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Erschienen in:
Beyond the Second Law: An Overview Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

5. Fluctuations, Trajectory Entropy and Ziegler’s Maximum Entropy Production Principle

verfasst von : Vladimir D. Seleznev, Leonid M. Martyushev

Erschienen in: Beyond the Second Law

Verlag: Springer Berlin Heidelberg

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Abstract

This chapter discusses two current interpretations of the maximum entropy production principle—as a physical principle and as an inference procedure. A simple model of relaxation of an isolated system towards equilibrium is considered for this purpose.

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Vorheriges Kapitel Dissipation Rate Functions, Pseudopotentials, Potentials and Yield Surfaces
Nächstes Kapitel The Time Evolution of Entropy Production in Nonlinear Dynamic Systems
Fußnoten
1
According to their definitions [27‐29], γ ii  > 0 and γ11γ22−γ 12 2  ≥ 0.
 
2
For small τ values: β ij Δα i Δα j  ≪ γ ij Δα i Δα j * (because γ ij  = γ ij 0 /τ).
 
3
For small τ values: dα i * /dt ≈ −Δα i * /τ. The minus sign arises from the fact that Δα i * is the difference between the initial and final value.
 
4
For one approximation, extremization is carried out for a random deviation from the equilibrium, whereas for the other approximation, it is carried out for a thermodynamic flux, i.e. the most probable deviation.
 
5
Mathematical models are absolutely unsuitable for falsification. So, a model is only some more or less crude and often one-sided reflection of some part of a phenomenon, whereas MEPP is the principle reflecting the dissipative properties that are observed in nature rather than in its model.
 
6
Indeed, the researcher’s intention to mathematically make the most unprejudiced prediction in the conditions of incomplete information about the system is the essence of this method. Therefore, if a phenomenon is very poorly experimentally studied (i.e. there are insufficient constraints), then anything can be predicted using MaxEnt (i.e. there are no truth criteria). In contrast, when MaxEP or MaxEnt are considered as physical principles, there are far fewer possibilities for drawing arbitrary conclusions. Methods that predict something specific for poorly studied phenomena (from which their falsifiability derives) are especially valuable.
 
7
If this cannot be achieved by selecting the constraints, then other kinds of informational entropy can always be used, for example, by Tsallis, Abe, Kullback, and many others [23, 30].
 
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Metadaten
Titel
Fluctuations, Trajectory Entropy and Ziegler’s Maximum Entropy Production Principle
verfasst von
Vladimir D. Seleznev
Leonid M. Martyushev
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Buch
Beyond the Second Law

Print ISBN: 978-3-642-40153-4

Electronic ISBN: 978-3-642-40154-1

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-642-40154-1_5