scholarly journals Erratum to: Non-equilibrium thermodynamics and maximum entropy production in the earth system: Applications and implications

2010 ◽  
Vol 97 (12) ◽  
pp. 1123-1123 ◽  
Author(s):  
Axel Kleidon
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Earth System ◽  
Equilibrium Thermodynamics ◽  
Maximum Entropy Production ◽  
The Earth ◽  
Non Equilibrium

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.

scholarly journals The maximum entropy production principle: two basic questions

2010 ◽  
Vol 365 (1545) ◽  
pp. 1333-1334 ◽  
Author(s):  
Leonid M. Martyushev
Keyword(s):  
Statistical Mechanics ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Physics ◽  
Overwhelming Majority ◽  
Equilibrium Thermodynamics ◽  
Maximum Entropy Production ◽  
Environmental Systems ◽  
Thermodynamics And Statistical Mechanics ◽  
Non Equilibrium

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to ‘prove’ the principle? We adduce one more proof which is most concise today.

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 Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy

2015 ◽  
Vol 22 (2) ◽  
pp. 187-196 ◽  
Author(s):  
M. Mihelich ◽  
D. Faranda ◽  
B. Dubrulle ◽  
D. Paillard
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Passive Scalar ◽  
Scalar Transport ◽  
Zero Range Process ◽  
Maximum Entropy Production ◽  
Passive Scalar Transport ◽  
Optimal Resolution ◽  
Principle Of Maximum ◽  
Non Equilibrium

Abstract. 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.

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.

Sign in / Sign up

Export Citation Format

Share Document