scholarly journals Maximum entropy production: can it be used to constrain conceptual hydrological models?

2012 ◽  
Vol 9 (10) ◽  
pp. 11551-11581
Author(s):  
M. C. Westhoff ◽  
E. Zehe
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Hydrological Models ◽  
Model Concept ◽  
Maximum Entropy Production ◽  
Principle Of Maximum Entropy ◽  
Optimality Principles ◽  
The Right ◽  
Principle Of Maximum

Abstract. In recent years, optimality principles have been proposed to constrain hydrological models. The principle of Maximum Entropy Production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. However, within hydrology, tests against observations are still missing. The aim of this paper is to test the MEP principle to reduce equifinality of a simple conceptual (bucket) model. We used the principle of maximizing power, which is equivalent to MEP when a constant temperature is assumed. Power is determined by multiplying a flux with its gradient. We thus defined for each flux in the model a gradient and checked if parameter sets that maximize power also reproduce the observed water balance. Subsequently we concluded that with the used model concept, this does not work. It would be easy to reject the MEP hypothesis to explain our findings, but we believe that our test is incomplete. By referring to the flaws in our own model concept, we believe that many issues can be learned about how to use MEP to constrain hydrological models. Among others, the most important are: (1) fluxes should be defined as a gradient divided by a resistance, where the flux feeds back on the gradient; (2) there should be a trade-off between two or more different fluxes, where, in principle, only one resistance can be optimized and (3) each process should have the right degrees of freedom: what are the feedbacks on this flux and what limits the flux?

scholarly journals Maximum entropy production: can it be used to constrain conceptual hydrological models?

2013 ◽  
Vol 17 (8) ◽  
pp. 3141-3157 ◽  
Author(s):  
M. C. Westhoff ◽  
E. Zehe
Keyword(s):  
Boundary Conditions ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Maximum Power ◽  
Hydrological Models ◽  
Maximum Entropy Production ◽  
Physically Based ◽  
Maximum Power Principle ◽  
Optimality Principles ◽  
Principle Of Maximum

Abstract. In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in literature, generally little guidance has been given on how to apply the principle. The aim of this paper is to use the maximum power principle – which is closely related to MEP – to constrain parameters of a simple conceptual (bucket) model. Although, we had to conclude that conceptual bucket models could not be constrained with respect to maximum power, this study sheds more light on how to use and how not to use the principle. Several of these issues have been correctly applied in other studies, but have not been explained or discussed as such. While other studies were based on resistance formulations, where the quantity to be optimized is a linear function of the resistance to be identified, our study shows that the approach also works for formulations that are only linear in the log-transformed space. Moreover, we showed that parameters describing process thresholds or influencing boundary conditions cannot be constrained. We furthermore conclude that, in order to apply the principle correctly, the model should be (1) physically based; i.e. fluxes should be defined as a gradient divided by a resistance, (2) the optimized flux should have a feedback on the gradient; i.e. the influence of boundary conditions on gradients should be minimal, (3) the temporal scale of the model should be chosen in such a way that the parameter that is optimized is constant over the modelling period, (4) only when the correct feedbacks are implemented the fluxes can be correctly optimized and (5) there should be a trade-off between two or more fluxes. Although our application of the maximum power principle did not work, and although the principle is a hypothesis that should still be thoroughly tested, we believe that the principle still has potential in advancing hydrological science.

scholarly journals A Statistical Inference of the Principle of Maximum Entropy Production

2021 ◽  
Author(s):  
Martijn Veening
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Inference ◽  
Explanatory Power ◽  
Second Law Of Thermodynamics ◽  
General Validity ◽  
Maximum Entropy Production ◽  
Principle Of Maximum Entropy ◽  
Theoretical Paper ◽  
Principle Of Maximum

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

scholarly journals The two-box model of climate: limitations and applications to planetary habitability and maximum entropy production studies

2010 ◽  
Vol 365 (1545) ◽  
pp. 1349-1354 ◽  
Author(s):  
Ralph D. Lorenz
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Box Model ◽  
Maximum Entropy Production ◽  
First Order ◽  
Production Studies ◽  
Principle Of Maximum Entropy ◽  
Temperature Contrast ◽  
Planetary Habitability ◽  
Principle Of Maximum

The ‘two-box model’ of planetary climate is discussed. This model has been used to demonstrate consistency of the equator–pole temperature gradient on Earth, Mars and Titan with what would be predicted from a principle of maximum entropy production (MEP). While useful for exposition and for generating first-order estimates of planetary heat transports, it has too low a resolution to investigate climate systems with strong feedbacks. A two-box MEP model agrees well with the observed day : night temperature contrast observed on the extrasolar planet HD 189733b.

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