Kirchhoff’s loop law and the maximum entropy production principle

Županović, Paško; Juretić, Davor; Botrić, Srećko

doi:10.1103/physreve.70.056108

Cited by 61 publications

(72 citation statements)

References 28 publications

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“…If we express hydrologic fluxes as an electric network of resistances (e.g., as in Fig. 4), then this would follow directly from Kirchhoff's loop law, which in turn has been derived from the assumption that currents are partitioned to maximize entropy production (Zupanovic et al 2004). …”

Section: Demonstration Of Mep States: Examplesmentioning

confidence: 99%

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

Kleidon

2009

Naturwissenschaften

150

123

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The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies A. Kleidon (B) Max-Planck-Institut für Biogeochemie, Postfach 10 01 64, 07701 Jena, Germany e-mail: akleidon@bgc-jena.mpg.de that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.

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Section: Demonstration Of Mep States: Examplesmentioning

confidence: 99%

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

Kleidon

2009

Naturwissenschaften

150

123

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“…This could, for instance, be the case for a sufficiently complex network of many resistors that provide many alternative ways to dissipate potential gradients (see Zupanovic et al (2004) for a derivation of Kirchhoff's loop law from MEP). Given a certain, fixed internal resistance R G within the generator, the state of MEP then results from the tradeoff of a greater value of R 2 reducing the current I in the dissipation D = I 2 · R of the resistor R 2 (figure 2c).…”

Section: Characterizing Disequilibrium Of Earth-system Processes (A) mentioning

confidence: 99%

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

Kleidon

2010

Phil. Trans. R. Soc. A.

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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.

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“…It has been successfully applied to the problem of current distribution in linear electric networks [34,35] and flux distribution in the linear network of chemical reactions [36]. In spite of the fact that the MEP principle has not been theoretically rigorously proved [11,[37][38][39] it has been successfully applied in numerous problems in physics, chemistry and biology (see reference [11] and references therein).…”

Section: Discussionmentioning

confidence: 99%

Enzyme kinetics and the maximum entropy production principle

Dobovišek

Županović

Brumen

et al. 2011

Biophysical Chemistry

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A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition EP ES ↔ in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions EP ES → for three types of β -Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β -Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution..

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Kirchhoff’s loop law and the maximum entropy production principle

Cited by 61 publications

References 28 publications

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

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

Enzyme kinetics and the maximum entropy production principle

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