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| Titel |
Statistical optimization for passive scalar transport: maximum entropy production vs. maximum Kolmogorov-Sinay entropy |
| VerfasserIn |
M. Mihelich, D. Faranda, B. Dubrulle, D. Paillard |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 1, no. 2 ; Nr. 1, no. 2 (2014-11-18), S.1691-1713 |
| Datensatznummer |
250115131
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| Publikation (Nr.) |
 copernicus.org/npgd-1-1691-2014.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 using 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 f admit a unique maximum denoted
fmaxEP and fmaxKS. The behavior of
these two maxima is explored as a function of the system
disequilibrium and the system resolution N. The main result of
this article is that fmaxEP and fmaxKS
have the same Taylor expansion at first order in the deviation of
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 that adopted by Paltridge and
climatologists (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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