What did Lotka really say? A critical reassessment of the “maximum power principle”

2011 ◽  
Vol 222 (8) ◽  
pp. 1347-1353 ◽  
Author(s):  
Enrico Sciubba
Keyword(s):  
Maximum Power ◽  
Maximum Power Principle

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 Can the “Maximum Power Principle” Be Applied to Pulsed Dielectric Barrier Discharge?

2019 ◽  
Vol 47 (8) ◽  
pp. 4052-4057
Author(s):  
Danil Dobrynin ◽  
Dmitri Vainchtein ◽  
Matteo Gherardi ◽  
Vittorio Colombo ◽  
Alexander Fridman
Keyword(s):  
Dielectric Barrier Discharge ◽  
Barrier Discharge ◽  
Maximum Power ◽  
Dielectric Barrier ◽  
Maximum Power Principle

scholarly journals Does the Budyko curve reflect a maximum-power state of hydrological systems? A backward analysis

2016 ◽  
Vol 20 (1) ◽  
pp. 479-486 ◽  
Author(s):  
M. Westhoff ◽  
E. Zehe ◽  
P. Archambeau ◽  
B. Dewals
Keyword(s):  
Maximum Power ◽  
Actual Evaporation ◽  
Run Off ◽  
Maximum Power Principle ◽  
State Behaviour ◽  
Backward Analysis ◽  
Almost All ◽  
Future Work ◽  
Principle Of Maximum ◽  
Organizing Principles

Abstract. Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving run-off and evaporation for a simple one-box model. We did this in an inverse manner such that, when the conductances are optimized with the maximum-power principle, the steady-state behaviour of the model leads exactly to a point on the asymptotes of the Budyko curve. Subsequently, we added dynamics in forcing and actual evaporation, causing the Budyko curve to deviate from the asymptotes. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves subject to observed dynamics in rainfall and actual evaporation. Thus by constraining the model that has been optimized with the maximum-power principle with the asymptotes of the Budyko curve, we were able to derive more realistic values of the aridity and evaporation index without any parameter calibration. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

The maximum power principle: An empirical investigation

2006 ◽  
Vol 190 (3-4) ◽  
pp. 317-335 ◽  
Author(s):  
T.T. Cai ◽  
C.L. Montague ◽  
J.S. Davis
Keyword(s):  
Empirical Investigation ◽  
Maximum Power ◽  
Maximum Power Principle

scholarly journals ESD Reviews: Thermodynamic optimality in Earth sciences. The missing constraints in modeling Earth system dynamics?

2019 ◽  
Author(s):  
Martijn Westhoff ◽  
Axel Kleidon ◽  
Stan Schymanski ◽  
Benjamin Dewals ◽  
Femke Nijsse ◽  
...  
Keyword(s):  
Earth Sciences ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Maximum Power ◽  
Model Parameters ◽  
Earth System ◽  
Maximum Entropy Production ◽  
Flux Gradient ◽  
Conversion Rates ◽  
Maximum Power Principle

Abstract. Thermodynamic optimality principles have been often used in Earth sciences to estimate model parameters or fluxes. Applications range from optimizing atmospheric meridional heat fluxes to sediment transport and from optimizing spatial flow patterns to dispersion coefficients for fresh and salt water mixing. However, it is not always clear what has to be optimized and how. In this paper we aimed to clarify terminology used in the literature and to infer how these principles have been used and when they give proper predictions of observed fluxes and states. We distinguish roughly four classes of applications: predictions using a flux-gradient feedback, predictions using a constant thermodynamic potential boundary conditions, predictions based on information theoretical approaches and comparative studies quantifying entropy production rates from observations at different sites. Here we mainly focus on the flux-gradient feedback, since it results in clear physical limits of energy conversion rates occurring in the Earth system and its subsystems. We show that within the flux-gradient feedback application, maximum entropy production is in many cases equivalent to maximum power and maximum energy dissipation. We advocate the maximum power principle above the more widely used maximum entropy production principle because entropy can be produced by all kinds of fluxes, but only optimized fluxes performing work coincided with observations. Furthermore, the maximum power principle links to the maximum amount of free energy that can be converted into another form of energy. This clearly separates the well defined physical conversion limit from the hypothesis that a system evolves to that limit of maximum power. Although attempts have been made to fundamentally explain why a system would evolve to such a maximum in power, there is still no consensus. Nevertheless, we think that when the maximum power approach is correctly and consistently used, the positive (or negative) results will speak for themselves. We end this review with some open research questions that may guide further research in this area.

scholarly journals Does the Budyko curve reflect a maximum power state of hydrological systems? A backward analysis

2015 ◽  
Vol 12 (8) ◽  
pp. 7821-7842
Author(s):  
M. Westhoff ◽  
E. Zehe ◽  
P. Archambeau ◽  
B. Dewals
Keyword(s):  
Maximum Power ◽  
Dry Spells ◽  
Maximum Power Principle ◽  
State Behaviour ◽  
Backward Analysis ◽  
Almost All ◽  
Future Work ◽  
Principle Of Maximum ◽  
Steady State Behaviour ◽  
Organizing Principles

Abstract. Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving runoff and evaporation for a simple one-box model. We did this in such a way that when the conductances are optimized with the maximum power principle, the steady state behaviour of the model leads exactly to a point on the Budyko curve. Subsequently we derived gradients that, under constant forcing, resulted in a Budyko curve following the asymptotes closely. With these gradients we explored the sensitivity of dry spells and dynamics in actual evaporation. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves derived with dynamics in rainfall and evaporation. This indicates that the maximum power principle may be used (i) to derive the Budyko curve and (ii) to move away from the empiricism in free parameters present in many Budyko functions. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

Taxi! The Modern Taxicab as Feminist Heterotopia

2014 ◽  
Vol 9 (2) ◽  
pp. 213-232
Author(s):  
Anne E. Fernald
Keyword(s):  
Virginia Woolf ◽  
Maximum Power ◽  
Male Gaze ◽  
Real Place ◽  
Critical Relation ◽  
Transitional Mode ◽  
Mode Of Transport ◽  
Woman's Body

The taxicab operated as a crucial transitional mode of transport for bourgeois women, allowing them maximum power as spectators when it was still brave for a woman to be a pedestrian. The writings of Virginia Woolf, which so often depict bourgeois women coping with modernity, form the chief context in which to explore the role of the taxicab in liberating the modern woman. The taxi itself, clumsy and ungendered, encases a woman's body and protects her from the male gaze. At the same time, a woman in a taxi can look out upon the street or freely ignore it. As such, the taxi is a type of heterotopia: a real place but one which functions outside of and in a critical relation to, the norms of the rest of the community.

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