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| Titel |
Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy |
| VerfasserIn |
M. Mihelich, D. Faranda, B. Dubrulle, D. Paillard |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 2 ; Nr. 22, no. 2 (2015-03-25), S.187-196 |
| Datensatznummer |
250120973
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| Publikation (Nr.) |
 copernicus.org/npg-22-187-2015.pdf |
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| Zusammenfassung |
| We derive rigorous results on the link between the principle of maximum
entropy production and the principle of maximum Kolmogorov–Sinai entropy for
a Markov model of the passive scalar diffusion called the Zero Range Process.
We show analytically that both the entropy production and the
Kolmogorov–Sinai entropy, seen as functions of a parameter f connected to
the jump probability, admit a unique maximum denoted fmaxEP and
fmaxKS. The behaviour of these two maxima is explored as a function of
the system disequilibrium and the system resolution N. The main result of
this paper is that fmaxEP and fmaxKS have the same Taylor
expansion at first order in the deviation from equilibrium. We find that
fmaxEP hardly depends on N whereas fmaxKS depends strongly
on N. In particular, for a fixed difference of potential between the
reservoirs, fmaxEP(N) tends towards a non-zero value, while
fmaxKS(N) tends to 0 when N goes to infinity. For values of N
typical of those adopted by Paltridge and climatologists working on maximum entropy production
(N ≈ 10–100), we show that fmaxEP and fmaxKS
coincide even far from equilibrium. Finally, we show that one can find an
optimal resolution N* such that fmaxEP and fmaxKS
coincide, at least up to a second-order parameter proportional to the
non-equilibrium fluxes imposed to the boundaries. We find that the optimal
resolution N* depends on the non-equilibrium fluxes, so that deeper
convection should be represented on finer grids. This result points to the
inadequacy of using a single grid for representing convection in climate and
weather models. Moreover, the application of this principle to passive scalar
transport parametrization is therefore expected to provide both the value of
the optimal flux, and of the optimal number of degrees of freedom
(resolution) to describe the system. |
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