scholarly journals A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production

2010 ◽  
Vol 365 (1545) ◽  
pp. 1303-1315 ◽  
Author(s):  
A. Kleidon
Keyword(s):  
Boundary Conditions ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Earth System ◽  
Maximum Entropy Production ◽  
The Earth ◽  
Far From Equilibrium ◽  
Global Cycles ◽  
Thermodynamic Basis

The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion.

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 Maximum entropy production in environmental and ecological systems

2010 ◽  
Vol 365 (1545) ◽  
pp. 1297-1302 ◽  
Author(s):  
Axel Kleidon ◽  
Yadvinder Malhi ◽  
Peter M. Cox
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Atmospheric Composition ◽  
Maximum Entropy Production ◽  
Gaia Hypothesis ◽  
Atmosphere System ◽  
Global Biogeochemical Cycles ◽  
Principle Of Maximum ◽  
Thermodynamic Processes

The coupled biosphere–atmosphere system entails a vast range of processes at different scales, from ecosystem exchange fluxes of energy, water and carbon to the processes that drive global biogeochemical cycles, atmospheric composition and, ultimately, the planetary energy balance. These processes are generally complex with numerous interactions and feedbacks, and they are irreversible in their nature, thereby producing entropy. The proposed principle of maximum entropy production (MEP), based on statistical mechanics and information theory, states that thermodynamic processes far from thermodynamic equilibrium will adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate. This issue focuses on the latest development of applications of MEP to the biosphere–atmosphere system including aspects of the atmospheric circulation, the role of clouds, hydrology, vegetation effects, ecosystem exchange of energy and mass, biogeochemical interactions and the Gaia hypothesis. The examples shown in this special issue demonstrate the potential of MEP to contribute to improved understanding and modelling of the biosphere and the wider Earth system, and also explore limitations and constraints to the application of the MEP 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.

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution

2010 ◽  
Vol 368 (1910) ◽  
pp. 181-196 ◽  
Author(s):  
Axel Kleidon
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Thermodynamic Equilibrium ◽  
Earth System ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
System Evolution ◽  
The Earth ◽  
System Functioning ◽  
Non Equilibrium

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system’s state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth’s past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning.

The mechanics of granitoid systems and maximum entropy production rates

2010 ◽  
Vol 368 (1910) ◽  
pp. 53-93 ◽  
Author(s):  
Bruce E. Hobbs ◽  
Alison Ord
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Melt Inclusions ◽  
Selection Process ◽  
Finite Thickness ◽  
Control Valve ◽  
Entropy Production Rate ◽  
Constitutive Behaviour ◽  
Maximum Entropy Production ◽  
Physical Height

A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10 4 –10 7 years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson–Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient ‘ponds’ of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic–viscous at high temperatures to elastic–plastic–viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate.

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