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

Kleidon, Axel

doi:10.1098/rstb.2009.0310

Cited by 77 publications

(82 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The analysis of the "horizontal"Ṡ hor and "vertical" S ver component of the material entropy production shows thatṠ hor is almost independent of the vertical heat fluxes. SinceṠ hor is entirely due to atmospheric processes, this result is consistent with the maximum power conjecture discussed in Kleidon (2010) in terms of a two-box model (as the mechanical power dissipated by the climate system is almost entirely associated with the atmospheric circulation). Also, S ver is independent of the horizontal heat flux M i.e.…”

Section: Discussionsupporting

confidence: 78%

“…Since then there has been a long and lively debate on MEP. This conjecture, often controversial (Goody, 2007;Caldeira, 2007;Nicolis and Nicolis, 2010), has been mainly tested through simple energy-balance boxmodels (Paltridge, 1975(Paltridge, , 1978(Paltridge, , 1981Grassl, 1981;Noda and Tokioka, 1983;Lorenz et al, 2001;Pujol and Fort, 2002;Pujol, 2003;Kleidon, 2004Kleidon, , 2010Jupp and Cox, 2010;Herbert et al, 2011a) and, in a few cases, general circulation models (Kleidon et al, 2003(Kleidon et al, , 2006Ito and Kleidon, 2005;Kunz et al, 2008;Pascale et al, 2011b) whereas a rigorous mathematical proof is still missing (Dewar, 2005;Grinstein and Linsker, 2007). Therefore despite some evidence which has built up in geosciences and despite its attraction of offering a beautiful unifying picture for all disequilibrium processes in the Earth system (Kleidon, 2010) and for the several co-related extremal principles known in Fluid Dynamics (Malkus, 1954(Malkus, , 1956(Malkus, , 2003Lorenz, 1960;Busse, 1969Busse, , 1970, MEP still has a shadowy theoretical foundation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

et al. 2012

View full text Add to dashboard Cite

Abstract. The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m −2 K −1 of material entropy production is due to vertical heat transport and 5-7 mW m −2 K −1 to horizontal heat transport.

show abstract

Section: Discussionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

et al. 2012

View full text Add to dashboard Cite

show abstract

“…That depends on how MEP theory is formulated. Currently, MEP theory admits that constraints can prevent systems from reaching the MEP state (Kleidon 2010). When the nature of these constraints becomes part of the theory itself, we suggest that some basic difference in the 'rules' for applying MEP will emerge between physical-chemical systems and those containing biology.…”

Section: Entropy-how You Produce It T Volk and O Pauluis 1319mentioning

confidence: 99%

It is not the entropy you produce, rather, how you produce it

Volk

Pauluis

2010

Phil. Trans. R. Soc. B

View full text Add to dashboard Cite

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will 'adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate'. Our aim in this 'outside view', invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physicalchemical systems and also systems governed by the 'laws' of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

show abstract

“…This issue starts with a basic introduction to the far from equilibrium thermodynamics of the Earth system by Kleidon (2010). This paper reviews the basics of thermodynamics to demonstrate that thermodynamics provides the means of describing practically all Earth system processes in purely thermodynamic terms.…”

Section: Contents Of This Issuementioning

confidence: 99%

Maximum entropy production in environmental and ecological systems

Kleidon

Malhi

Cox

2010

Phil. Trans. R. Soc. B

152

107

View full text Add to dashboard Cite

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.Keywords: thermodynamics; interactions; Earth system science; ecosystems THERMODYNAMICS AND ENVIRONMENTAL AND ECOLOGICAL SYSTEMSThermodynamics has long been recognized as critical for understanding complex systems ranging from the living cell to planet Earth (Boltzmann 1886;Schrö dinger 1944;Lovelock 1965). Boltzmann already noted in 1886 that:. . . the general struggle for existence of animate beings is not a struggle for raw materials-these, for organisms, are air, water and soil, all abundantly available, nor for energy which exists in plenty in any body in the form of heat, but a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold Earth.Schrö dinger (1944) extended this perspective in his seminal book What is life? in which he suggested that the living cell maintains its organized structure in a state of thermodynamic disequilibrium by depleting sources of free energy and exporting high entropy waste. At the planetary scale, Lovelock (1965) recognized that the Earth's atmospheric composition is maintained in a state far from thermodynamic equilibrium, and he attributed this unique thermodynamic state to the profound effect that life has on its environment.Taken together, these examples suggest that in order to better understand Earth's environmental and ecological systems and their couplings, we need to view these as coupled thermodynamic systems that are organized in a state far from thermodynamic equilibrium. Central to thermodynamics is the concept of 'entropy' as a measure of 'disorder' or 'randomness'. While the use of 'entropy' is often surrounded with ambiguity, it can nevertheless be used in purely quantitative terms to measure the distance of a given state from thermodynamic equilibriu...

show abstract

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

Cited by 77 publications

References 40 publications

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

It is not the entropy you produce, rather, how you produce it

Maximum entropy production in environmental and ecological systems

Contact Info

Product

Resources

About