State Of Maximum Entropy Production Research Articles

Assessing the Complementary Role of Surface Flux Equilibrium (SFE) Theory and Maximum Entropy Production (MEP) Principle in the Estimation of Actual Evapotranspiration

AbstractAlthough evapotranspiration (ET) from the land is a key variable in Earth system models, the accurate estimation of ET based on physical principles remains challenging. Parameters used in current ET models are largely empirically based, which could be problematic under rapidly changing climatic conditions. Here, we propose a physically based ET model that estimates ET based on the surface flux equilibrium (SFE) theory and the maximum entropy production (MEP) principle. We derive an expression for aerodynamic resistance based on the MEP principle, then propose a novel ET model that integrates the SFE model and the MEP principle. The proposed model, which is referred to as the SFE‐MEP model, becomes equivalent to the MEP state in non‐equilibrium conditions when turbulent mixing is weak and the land surface is dry. Under conditions meeting land‐atmosphere equilibrium, the SFE‐MEP model is similar to ET estimation based on the SFE model. This blended nature of the SFE‐MEP ET model allows accurate ET estimation for most inland regions by overcoming the ET overestimation issue of the SFE model in dry conditions. As a result, the SFE‐MEP model significantly improves the performance of SFE ET estimation, particularly for arid regions. The proposed model and its high accuracy of ET estimation enable novel insight into various Earth system models as it does not require any empirical parameters and only uses readily obtainable meteorological variables including reference height air temperature, relative humidity, available energy, and radiometric surface temperature.

Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection

Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport). This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of heat flux and temperature difference F / Δ T —which is proportional to the dimensionless Nusselt number—does appear to be maximized.

The Role of Vegetation on the Ecosystem Radiative Entropy Budget and Trends Along Ecological Succession

Ecosystem entropy production is predicted to increase along ecological succession and approach a state of maximum entropy production, but few studies have bridged the gap between theory and data. Here, we explore radiative entropy production in terrestrial ecosystems using measurements from 64 Free/Fair-Use sites in the FLUXNET database, including a successional chronosequence in the Duke Forest in the southeastern United States. Ecosystem radiative entropy production increased then decreased as succession progressed in the Duke Forest ecosystems, and did not exceed 95% of the calculated empirical maximum entropy production in the FLUXNET study sites. Forest vegetation, especially evergreen needleleaf forests characterized by low shortwave albedo and close coupling to the atmosphere, had a significantly higher ratio of radiative entropy production to the empirical maximum entropy production than did croplands and grasslands. Our results demonstrate that ecosystems approach, but do not reach, maximum entropy production and that the relationship between succession and entropy production depends on vegetation characteristics. Future studies should investigate how natural disturbances and anthropogenic management—especially the tendency to shift vegetation to an earlier successional state—alter energy flux and entropy production at the surface-atmosphere interface.

The energetics of ecological succession: A logistic model of entropic output

The maximum entropy production principle (MEPP) is an important and growing area of research with significant implications for many fields of study, including ecology. Thermodynamically, an ecosystem operates in such a way as to maximize entropic production, in accordance with the second law of thermodynamics. This paper presents a general model of the observed changes in entropic production during ecological succession, beginning with emerging evidence that the climax community represents a state of maximum entropy production. We then examine the outcome of this model, which provides a new insight into the driving process, direction and seral progression observed in succession. We suggest that succession moves towards an energetic rather than a structural climax, which represents a dynamic rather than a static state. Using the maximum entropy production principle, we propose that entropic generation across a succession follows a logistic model, initially undergoing rapid increase in entropy production, before approaching an asymptote, called Smax. The underlying changes in entropy production are suggested to control seral change. This is in agreement with a growing body of literature, and provides a framework for a new understanding of succession. These findings also have significant implications for assessing anthropological impacts on ecosystems.

Metabolic networks evolve towards states of maximum entropy production

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles.

Present and Last Glacial Maximum climates as states of maximum entropy production

AbstractThe Earth, like other planets with a relatively thick atmosphere, is not locally in radiative equilibrium and the transport of energy by the geophysical fluids (atmosphere and ocean) plays a fundamental role in determining its climate. Using simple energy‐balance models, it was suggested a few decades ago that the meridional energy fluxes might follow a thermodynamic Maximum Entropy Production (MEP) principle. In the present study, we assess the MEP hypothesis in the framework of a minimal climate model based solely on a robust radiative scheme and the MEP principle, with no extra assumptions. Specifically, we show that by choosing an adequate radiative exchange formulation, the Net Exchange Formulation, a rigorous derivation of all the physical parameters can be performed. The MEP principle is also extended to surface energy fluxes, in addition to meridional energy fluxes. The climate model presented here is extremely fast, needs very little empirical data and does not rely on ad hoc parameterizations. We investigate its range of validity by comparing its performances for pre‐industrial climate and Last Glacial Maximum climate with corresponding simulations with the IPSL coupled atmosphere‐ocean General Circulation Model IPSL_CM4, finding reasonable agreement. Beyond the practical interest of this result for climate modelling, it supports the idea that, to a certain extent, climate can be characterized by macroscale features with no need to compute the underlying microscale dynamics. Copyright © 2011 Royal Meteorological Society

Enzyme kinetics and the maximum entropy production principle

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 ES ↔ EP 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 ES → EP 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 a 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.

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

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 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.

Maximum entropy production and plant optimization theories.

Plant ecologists have proposed a variety of optimization theories to explain the adaptive behaviour and evolution of plants from the perspective of natural selection ('survival of the fittest'). Optimization theories identify some objective function--such as shoot or canopy photosynthesis, or growth rate--which is maximized with respect to one or more plant functional traits. However, the link between these objective functions and individual plant fitness is seldom quantified and there remains some uncertainty about the most appropriate choice of objective function to use. Here, plants are viewed from an alternative thermodynamic perspective, as members of a wider class of non-equilibrium systems for which maximum entropy production (MEP) has been proposed as a common theoretical principle. I show how MEP unifies different plant optimization theories that have been proposed previously on the basis of ad hoc measures of individual fitness--the different objective functions of these theories emerge as examples of entropy production on different spatio-temporal scales. The proposed statistical explanation of MEP, that states of MEP are by far the most probable ones, suggests a new and extended paradigm for biological evolution--'survival of the likeliest'--which applies from biomacromolecules to ecosystems, not just to individuals.

MEP and planetary climates: insights from a two-box climate model containing atmospheric dynamics

A two-box model for equator-to-pole planetary heat transport is extended to include simple atmospheric dynamics. The surface drag coefficient CD is treated as a free parameter and solutions are calculated analytically in terms of the dimensionless planetary parameters eta (atmospheric thickness), omega (rotation rate) and xi (advective capability). Solutions corresponding to maximum entropy production (MEP) are compared with solutions previously obtained from dynamically unconstrained two-box models. As long as the advective capability xi is sufficiently large, dynamically constrained MEP solutions are identical to dynamically unconstrained MEP solutions. Consequently, the addition of a dynamical constraint does not alter the previously obtained MEP results for Earth, Mars and Titan, and an analogous result is presented here for Venus. The rate of entropy production in an MEP state is shown to be independent of rotation rate if the advective capability xi is sufficiently large (as for the four examples in the solar system), or if the rotation rate omega is sufficiently small. The model indicates, however, that the dynamical constraint does influence the MEP state when xi is small, which might be the case for some extrasolar planets. Finally, results from the model developed here are compared with previous numerical simulations in which the effect of varying surface drag coefficient on entropy production was calculated.

Entropy production and self-organized (sub)criticality in earthquake dynamics

We derive an analytical expression for entropy production in earthquake populations based on Dewar's formulation, including flux (tectonic forcing) and source (earthquake population) terms, and apply it to the Olami-Feder-Christensen numerical model for earthquake dynamics. Assuming the commonly observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production (MEP) is a thermodynamic driver for self-organized 'criticality' (SOC) in the model. MEP occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC (which has, to date, often included self-organizing systems in a near but strictly subcritical state). In the MEP state, the strain field retains some memory of past events, expressed as coherent 'domains', implying a degree of predictability, albeit strongly limited in practice by the proximity to criticality and our inability to map the natural stress field at an equivalent resolution to the numerical model.

A Story and a Recommendation about the Principle of Maximum Entropy Production

The principle of maximum entropy production (MEP) is the subject of considerable academic study, but has yet to become remarkable for its practical applications. A tale is told of an instance in which a spin-off from consideration of an MEP-constrained climate model at least led to re-consideration of the very practical issue of water-vapour feedback in climate change. Further, and on a more-or-less unrelated matter, a recommendation is made for further research on whether there might exist a general "rule" whereby, for certain classes of complex non-linear systems, a state of maximum entropy production is equivalent to a state of minimum entropy.

Nonequilibrium thermodynamics and maximum entropy production in the Earth system

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 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.

Cloud and Water Vapor Feedbacks in a Vertical Energy-Balance Model with Maximum Entropy Production

AbstractA vertically one-dimensional model is developed with cloud fraction constrained by the maximum entropy production (MEP) principle. The model reasonably reproduces the global mean climate with its surface temperature, radiation and heat fluxes, cloud fraction, and lapse rate. The maximum convection hypothesis in Paltridge’s models is related to the MEP principle, and the MEP state of climate is approximately equivalent to that with the maximum lapse rate. The sensitivity investigation about the model assumptions and the prescribed parameters show that the model is considerably robust in simulating the global mean climate. With the MEP constraint, the feedbacks of cloud and water vapor to external forcings, such as changes of CO2 concentration, solar incidence, and surface albedo, are evaluated. While water vapor always behaves as a strong positive feedback, cloud feedbacks to the different forcings are different, in both magnitude and sign. The modeled feedback of cloud fraction to the forcing resulting from surface albedo variation seems in good agreement with the observed seasonal variation of the global cloud fraction.

An optimal principle in fluid–structure interaction

We study the steady terminal orientation of a fore-aft symmetric body as it settles in a viscous fluid. An optimal principle for the settling behavior is discussed based upon entropy production in the system, both in the Stokes limit and the case of near equilibrium states when inertial effects emerge. We show that in the Stokes limit, the entropy production in the system is zero allowing any possible terminal orientation while in the presence of inertia, the particle assumes a horizontal position which coincides with the state of maximum entropy production. Our results are seen to agree well with experimental observations.

The properties of organisms are not tunable parameters selected because they create maximum entropy production on the biosphere scale: A by-product framework in response to Kleidon

Axel Kleidon (Clim Change 66:271–319, 2004) proposed that the organisms that constitute Earth’s biota have free parameters that can be selected to create states of maximum entropy production (MEP) on various scales, from the biota to the planetary radiation balance of the Earth system. I show that Kleidon’s concept, here called the biotic-MEP hypothesis, is fundamentally mistaken. A thought experiment with a life form that would be selected against even though it would generate a higher degree of entropy demonstrates my case: A hypothetical tree that puts forth a non-productive but high-entropy producing black carpet of tissue clearly separates out entropy production from other biological processes and shows that entropy production is not a functional adaptation and therefore it cannot be selected for. A real world example comes from dimethyl sulfide-emitting plankton, which, by increasing cloud albedo, do not raise but rather lower the entropy flux of the Earth system. I provide a number of other examples of biotic processes that individually either decrease or increase the environmental entropy production. It is argued that biological effects on environmental entropy production can be expected to include both positive and negative examples, because these effects are merely by-products of the actual processes that are selected for by evolution. Given my framework of entropy production as a by-product of the true processes that are being selected for, the concept of MEP on environmental scales has no great relevance for discussions of biological evolution or the time history of the effects of life on the global system.

Maximum Entropy Production in Climate Theory

AbstractR. D. Lorenz et al. claim that recent data on Mars and Titan show that planetary atmospheres are in unconstrained states of maximum entropy production (MEP). Their model as it applies to Venus, Earth, Mars, and Titan is reexamined, and it is shown that their claim is not justified. This does not necessarily imply that MEP is incorrect, and inapplicable to atmospheres, but it does mean that the difficult and unexplored problem of dynamical constraints on the MEP solution must be understood if it is to be of value for climate research.

Kirchhoff’s loop law and the maximum entropy production principle

In contrast to the standard derivation of Kirchhoff's loop law, which invokes electric potential, we show, for the linear planar electric network in a stationary state at the fixed temperature, that loop law can be derived from the maximum entropy production principle. This means that the currents in network branches are distributed in such a way as to achieve the state of maximum entropy production.

Beyond Gaia: Thermodynamics of Life and Earth System Functioning

Are there any general principles that govern the way in which life affects Earth system functioning? Most prominently, the Gaia hypothesis addresses this question by proposing that near-homeostatic conditions on Earth have been maintained “by and for the biosphere.” Here the role of the biota in the Earth system is described from a viewpoint of nonequilibrium thermodynamics, particularly with respect to the hypothesis of maximum entropy production (MEP). It is argued that the biota introduce additional degrees of freedom to Earth system processes. Therefore, we should expect biotic activity, and Earth system processes affected by the biota, to evolve to states of MEP. The consistent effects of the biota on entropy production are demonstrated with a conceptual model of biogeochemical cycling, by using extreme climate model simulations of a “Desert World” and a “Green Planet”, and by a simple coupled climate-carbon cycle model. It is shown that homeostatic behavior can emerge from a state of MEP associated with the planetary albedo. This thermodynamic perspective is then discussed in the context of the original Gaia hypothesis and in light of a recent discussion in Climatic Change. Potential implications of the MEP hypothesis for global change research are also discussed. It is concluded that the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis. However, here homeostasis is a result of the application of the MEP hypothesis to biotically influenced processes rather than a postulate. Besides providing a fundamental perspective on homeostasis, the MEP hypothesis also provides a framework to understand why photosynthetic life would be a highly probable emergent characteristic of the Earth system and why the diversity of life is an important characteristic of Earth system functioning.

The atmospheric circulation and states of maximum entropy production

Energy balance models suggest that the atmospheric circulation operates close to a state of maximum entropy production. Here we support this hypothesis with sensitivity simulations of an atmospheric general circulation model. A state of maximum entropy production is obtained by (i) adjusting boundary layer turbulence and (ii) using a sufficiently high model resolution which allows sufficient degrees of freedom for the atmospheric flow. The state of maximum entropy production is associated with the largest conversion of available potential energy into kinetic energy which is subsequently dissipated by boundary layer turbulence. It exhibits the largest eddy activity in the mid latitudes, resulting in the most effective transport of heat towards the poles and the least equator‐pole temperature difference. These results suggest that GCMs have a fundamental tendency to underestimate the magnitude of atmospheric heat transport and, therefore, overestimate the equator‐pole temperature gradient for the present‐day climate, for the response to global climatic change, and for atmospheres of other planetary bodies.