Type of probability distribution reflects how close mixing dynamics in river chemistry are to thermodynamic equilibrium.

The distribution of geochemical species are typically either (log)normally distributed or follow power laws. Here we link these types of distributions to the dynamics of the system that generates these distributions, showing that power laws can emerge in dissipative systems far from equilibrium while (log)normal distributions are found for species for which the concentrations are close to equilibrium. We use observations of the chemical composition of river water from the sampling space in central Italy as well as discharge data to test this interpretation. We estimate the dissipation rate that results when groundwater drains into the river and the dissolved chemical species mix with the river water. We show that calcium (Ca2+) and bicarbonate (HCO3-) concentrations are close to saturation along most of the downstream length of the Arno river, with decreasing dissipation rates and a lognormal distribution, while sodium (Na+) and chloride (Cl-) concentrations increase substantially downstream, show increased dissipation rates, and are power-law distributed. This supports our hypothesis that power law distributions appear to be indicative of dissipative systems far from thermodynamic equilibrium, while (log)normal distributions indicate weakly dissipative systems close to equilibrium. What this implies is that probability distributions are likely to be indicative of the thermodynamics of the system and the magnitude of disequilibrium constrains the range over which power-law scaling may be observed. This should help us to better identify the generalities and mechanisms that result in these common types of distributions and to better classify variability in systems according to how dissipative these are.

Modeling cell populations metabolism and competition under maximum power constraints.

Ecological interactions are fundamental at the cellular scale, addressing the possibility of a description of cellular systems that uses language and principles of ecology. In this work, we use a minimal ecological approach that encompasses growth, adaptation and survival of cell populations to model cell metabolisms and competition under energetic constraints. As a proof-of-concept, we apply this general formulation to study the dynamics of the onset of a specific blood cancer-called Multiple Myeloma. We show that a minimal model describing antagonist cell populations competing for limited resources, as regulated by microenvironmental factors and internal cellular structures, reproduces patterns of Multiple Myeloma evolution, due to the uncontrolled proliferation of cancerous plasma cells within the bone marrow. The model is characterized by a class of regime shifts to more dissipative states for selectively advantaged malignant plasma cells, reflecting a breakdown of self-regulation in the bone marrow. The transition times obtained from the simulations range from years to decades consistently with clinical observations of survival times of patients. This irreversible dynamical behavior represents a possible description of the incurable nature of myelomas based on the ecological interactions between plasma cells and the microenvironment, embedded in a larger complex system. The use of ATP equivalent energy units in defining stocks and flows is a key to constructing an ecological model which reproduces the onset of myelomas as transitions between states of a system which reflects the energetics of plasma cells. This work provides a basis to construct more complex models representing myelomas, which can be compared with model ecosystems.

Radiative controls by clouds and thermodynamics shape surface temperatures and turbulent fluxes over land.

Land surface temperatures (LSTs) are strongly shaped by radiation but are modulated by turbulent fluxes and hydrologic cycling as the presence of water vapor in the atmosphere (clouds) and at the surface (evaporation) affects temperatures across regions. Here, we used a thermodynamic systems framework forced with independent observations to show that the climatological variations in LSTs across dry and humid regions are mainly mediated through radiative effects. We first show that the turbulent fluxes of sensible and latent heat are constrained by thermodynamics and the local radiative conditions. This constraint arises from the ability of radiative heating at the surface to perform work to maintain turbulent fluxes and sustain vertical mixing within the convective boundary layer. This implies that reduced evaporative cooling in dry regions is then compensated for by an increased sensible heat flux and buoyancy, which is consistent with observations. We show that the mean temperature variation across dry and humid regions is mainly controlled by clouds that reduce surface heating by solar radiation. Using satellite observations for cloudy and clear-sky conditions, we show that clouds cool the land surface over humid regions by up to 7 K, while in arid regions, this effect is absent due to the lack of clouds. We conclude that radiation and thermodynamic limits are the primary controls on LSTs and turbulent flux exchange which leads to an emergent simplicity in the observed climatological patterns within the complex climate system.

What limits photosynthesis? Identifying the thermodynamic constraints of the terrestrial biosphere within the Earth system.

Photosynthesis converts sunlight into the chemical free energy that feeds the Earth's biosphere, yet at levels much lower than what thermodynamics would allow for. I propose here that photosynthesis is nevertheless thermodynamically limited, but this limit acts indirectly on the material exchange. I substantiate this proposition for the photosynthetic activity of terrestrial ecosystems, which are notably more productive than the marine biosphere. The material exchange for terrestrial photosynthesis involves water and carbon dioxide, which I evaluate using global observation-based datasets of radiation, photosynthesis, precipitation and evaporation. I first calculate the conversion efficiency of photosynthesis in terrestrial ecosystems and its climatological variation, with a median efficiency of 0.77% (n = 13,274). The rates tightly correlate with evaporation on land (r2 = 0.87), which demonstrates the importance of the coupling of photosynthesis to material exchange. I then infer evaporation from the maximum material exchange between the surface and the atmosphere that is thermodynamically possible using datasets of solar radiation and precipitation. This inferred rate closely correlates with the observation-based land evaporation dataset (r2 = 0.84). When this rate is converted back into photosynthetic activity, the resulting patterns correlate highly with the observation-based dataset (r2 = 0.66). This supports the interpretation that it is not energy directly that limits terrestrial photosynthesis, but rather the material exchange that is driven by sunlight. This interpretation can explain the very low, observed conversion efficiency of photosynthesis in terrestrial ecosystems as well as its spatial variations. More generally, this implies that one needs to take the necessary material flows and exchanges associated with life into account to understand the thermodynamics of life. This, ultimately, requires a perspective that links the activity of the biosphere to the thermodynamic constraints of transport processes in the Earth system.

Uncertainty of runoff sensitivity to climate change in the Amazon River basin.

We employ the approach of Roderick and Farquhar (2011) to assess the sensitivity of runoff (R) given changes in precipitation (P), potential evapotranspiration (Ep ), and other properties that change the partitioning of P (n) by estimating coefficients that predict the weight of each variable in the relative change of R. We use this framework using different data sources and products for P, actual evapotranspiration (E), and Ep within the Amazon River basin to quantify the uncertainty of the hydrologic response at the subcatchment scale. We show that when estimating results from the different combinations of datasets for the entire river basin (at Óbidos), a 10% increase in P would increase R on average 16%, while a 10% increase in Ep would decrease R about 6%. In addition, a 10% change in the parameter n would affect the hydrological response of the entire basin around 5%. However, results change from catchment to catchment and are dependent on the combination of datasets. Finally, results suggest that enhanced estimates of E and Ep are needed to improve our understanding of the future scenarios of hydrological sensitivity with implications for the quantification of climate change impacts at the regional (subcatchment and subbasin) scale in Amazonia.

Have wind turbines in Germany generated electricity as would be expected from the prevailing wind conditions in 2000-2014?

The planning of the energy transition from fossil fuels to renewables requires estimates for how much electricity wind turbines can generate from the prevailing atmospheric conditions. Here, we estimate monthly ideal wind energy generation from datasets of wind speeds, air density and installed wind turbines in Germany and compare these to reported actual yields. Both yields were used in a statistical model to identify and quantify factors that reduced actual compared to ideal yields. The installed capacity within the region had no significant influence. Turbine age and park size resulted in significant yield reductions. Predicted yields increased from 9.1 TWh/a in 2000 to 58.9 TWh/a in 2014 resulting from an increase in installed capacity from 5.7 GW to 37.6 GW, which agrees very well with reported estimates for Germany. The age effect, which includes turbine aging and possibly other external effects, lowered yields from 3.6 to 6.7% from 2000 to 2014. The effect of park size decreased annual yields by 1.9% throughout this period. However, actual monthly yields represent on average only 73.7% of the ideal yields, with unknown causes. We conclude that the combination of ideal yields predicted from wind conditions with observed yields is suitable to derive realistic estimates of wind energy generation as well as realistic resource potentials.

Evaluation of climate-related carbon turnover processes in global vegetation models for boreal and temperate forests.

Turnover concepts in state-of-the-art global vegetation models (GVMs) account for various processes, but are often highly simplified and may not include an adequate representation of the dominant processes that shape vegetation carbon turnover rates in real forest ecosystems at a large spatial scale. Here, we evaluate vegetation carbon turnover processes in GVMs participating in the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP, including HYBRID4, JeDi, JULES, LPJml, ORCHIDEE, SDGVM, and VISIT) using estimates of vegetation carbon turnover rate (k) derived from a combination of remote sensing based products of biomass and net primary production (NPP). We find that current model limitations lead to considerable biases in the simulated biomass and in k (severe underestimations by all models except JeDi and VISIT compared to observation-based average k), likely contributing to underestimation of positive feedbacks of the northern forest carbon balance to climate change caused by changes in forest mortality. A need for improved turnover concepts related to frost damage, drought, and insect outbreaks to better reproduce observation-based spatial patterns in k is identified. As direct frost damage effects on mortality are usually not accounted for in these GVMs, simulated relationships between k and winter length in boreal forests are not consistent between different regions and strongly biased compared to the observation-based relationships. Some models show a response of k to drought in temperate forests as a result of impacts of water availability on NPP, growth efficiency or carbon balance dependent mortality as well as soil or litter moisture effects on leaf turnover or fire. However, further direct drought effects such as carbon starvation (only in HYBRID4) or hydraulic failure are usually not taken into account by the investigated GVMs. While they are considered dominant large-scale mortality agents, mortality mechanisms related to insects and pathogens are not explicitly treated in these models.

Wind speed reductions by large-scale wind turbine deployments lower turbine efficiencies and set low generation limits.

Wind turbines generate electricity by removing kinetic energy from the atmosphere. Large numbers of wind turbines are likely to reduce wind speeds, which lowers estimates of electricity generation from what would be presumed from unaffected conditions. Here, we test how well wind power limits that account for this effect can be estimated without explicitly simulating atmospheric dynamics. We first use simulations with an atmospheric general circulation model (GCM) that explicitly simulates the effects of wind turbines to derive wind power limits (GCM estimate), and compare them to a simple approach derived from the climatological conditions without turbines [vertical kinetic energy (VKE) estimate]. On land, we find strong agreement between the VKE and GCM estimates with respect to electricity generation rates (0.32 and 0.37 We m-2) and wind speed reductions by 42 and 44%. Over ocean, the GCM estimate is about twice the VKE estimate (0.59 and 0.29 We m-2) and yet with comparable wind speed reductions (50 and 42%). We then show that this bias can be corrected by modifying the downward momentum flux to the surface. Thus, large-scale limits to wind power use can be derived from climatological conditions without explicitly simulating atmospheric dynamics. Consistent with the GCM simulations, the approach estimates that only comparatively few land areas are suitable to generate more than 1 We m-2 of electricity and that larger deployment scales are likely to reduce the expected electricity generation rate of each turbine. We conclude that these atmospheric effects are relevant for planning the future expansion of wind power.

Physical Limits of Solar Energy Conversion in the Earth System.

Solar energy provides by far the greatest potential for energy generation among all forms of renewable energy. Yet, just as for any form of energy conversion, it is subject to physical limits. Here we review the physical limits that determine how much energy can potentially be generated out of sunlight using a combination of thermodynamics and observed climatic variables. We first explain how the first and second law of thermodynamics constrain energy conversions and thereby the generation of renewable energy, and how this applies to the conversions of solar radiation within the Earth system. These limits are applied to the conversion of direct and diffuse solar radiation - which relates to concentrated solar power (CSP) and photovoltaic (PV) technologies as well as biomass production or any other photochemical conversion - as well as solar radiative heating, which generates atmospheric motion and thus relates to wind power technologies. When these conversion limits are applied to observed data sets of solar radiation at the land surface, it is estimated that direct concentrated solar power has a potential on land of up to 11.6 PW (1 PW=10(15) W), whereas photovoltaic power has a potential of up to 16.3 PW. Both biomass and wind power operate at much lower efficiencies, so their potentials of about 0.3 and 0.1 PW are much lower. These estimates are considerably lower than the incoming flux of solar radiation of 175 PW. When compared to a 2012 primary energy demand of 17 TW, the most direct uses of solar radiation, e.g., by CSP or PV, have thus by far the greatest potential to yield renewable energy requiring the least space to satisfy the human energy demand. Further conversions into solar-based fuels would be reduced by further losses which would lower these potentials. The substantially greater potential of solar-based renewable energy compared to other forms of renewable energy simply reflects much fewer and lower unavoidable conversion losses when solar radiation is directly converted into renewable energy.

Two methods for estimating limits to large-scale wind power generation.

Wind turbines remove kinetic energy from the atmospheric flow, which reduces wind speeds and limits generation rates of large wind farms. These interactions can be approximated using a vertical kinetic energy (VKE) flux method, which predicts that the maximum power generation potential is 26% of the instantaneous downward transport of kinetic energy using the preturbine climatology. We compare the energy flux method to the Weather Research and Forecasting (WRF) regional atmospheric model equipped with a wind turbine parameterization over a 10(5) km2 region in the central United States. The WRF simulations yield a maximum generation of 1.1 We⋅m(-2), whereas the VKE method predicts the time series while underestimating the maximum generation rate by about 50%. Because VKE derives the generation limit from the preturbine climatology, potential changes in the vertical kinetic energy flux from the free atmosphere are not considered. Such changes are important at night when WRF estimates are about twice the VKE value because wind turbines interact with the decoupled nocturnal low-level jet in this region. Daytime estimates agree better to 20% because the wind turbines induce comparatively small changes to the downward kinetic energy flux. This combination of downward transport limits and wind speed reductions explains why large-scale wind power generation in windy regions is limited to about 1 We⋅m(-2), with VKE capturing this combination in a comparatively simple way.

Thermodynamics of random reaction networks.

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdos-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

The strengths of r- and K-selection shape diversity-disturbance relationships.

Disturbance is a key factor shaping species abundance and diversity in plant communities. Here, we use a mechanistic model of vegetation diversity to show that different strengths of r- and K-selection result in different disturbance-diversity relationships. R- and K-selection constrain the range of viable species through the colonization-competition tradeoff, with strong r-selection favoring colonizers and strong K-selection favoring competitors, but the level of disturbance also affects the success of species. This interplay among r- and K-selection and disturbance results in different shapes of disturbance-diversity relationships, with little variation of diversity with no r- and no K-selection, a decrease in diversity with r-selection with disturbance rate, an increase in diversity with K-selection, and a peak at intermediate values with strong r- and K-selection. We conclude that different disturbance-diversity relationships found in observations may reflect different intensities of r- and K-selection within communities, which should be inferable from broader observations of community composition and their ecophysiological trait ranges.

Carbon residence time dominates uncertainty in terrestrial vegetation responses to future climate and atmospheric CO2.

Future climate change and increasing atmospheric CO2 are expected to cause major changes in vegetation structure and function over large fractions of the global land surface. Seven global vegetation models are used to analyze possible responses to future climate simulated by a range of general circulation models run under all four representative concentration pathway scenarios of changing concentrations of greenhouse gases. All 110 simulations predict an increase in global vegetation carbon to 2100, but with substantial variation between vegetation models. For example, at 4 °C of global land surface warming (510-758 ppm of CO2), vegetation carbon increases by 52-477 Pg C (224 Pg C mean), mainly due to CO2 fertilization of photosynthesis. Simulations agree on large regional increases across much of the boreal forest, western Amazonia, central Africa, western China, and southeast Asia, with reductions across southwestern North America, central South America, southern Mediterranean areas, southwestern Africa, and southwestern Australia. Four vegetation models display discontinuities across 4 °C of warming, indicating global thresholds in the balance of positive and negative influences on productivity and biomass. In contrast to previous global vegetation model studies, we emphasize the importance of uncertainties in projected changes in carbon residence times. We find, when all seven models are considered for one representative concentration pathway × general circulation model combination, such uncertainties explain 30% more variation in modeled vegetation carbon change than responses of net primary productivity alone, increasing to 151% for non-HYBRID4 models. A change in research priorities away from production and toward structural dynamics and demographic processes is recommended.

How does the Earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?

The Earth's chemical composition far from chemical equilibrium is unique in our Solar System, and this uniqueness has been attributed to the presence of widespread life on the planet. Here, I show how this notion can be quantified using non-equilibrium thermodynamics. Generating and maintaining disequilibrium in a thermodynamic variable requires the extraction of power from another thermodynamic gradient, and the second law of thermodynamics imposes fundamental limits on how much power can be extracted. With this approach and associated limits, I show that the ability of abiotic processes to generate geochemical free energy that can be used to transform the surface-atmosphere environment is strongly limited to less than 1 TW. Photosynthetic life generates more than 200 TW by performing photochemistry, thereby substantiating the notion that a geochemical composition far from equilibrium can be a sign for strong biotic activity. Present-day free energy consumption by human activity in the form of industrial activity and human appropriated net primary productivity is of the order of 50 TW and therefore constitutes a considerable term in the free energy budget of the planet. When aiming to predict the future of the planet, we first note that since global changes are closely related to this consumption of free energy, and the demands for free energy by human activity are anticipated to increase substantially in the future, the central question in the context of predicting future global change is then how human free energy demands can increase sustainably without negatively impacting the ability of the Earth system to generate free energy. This question could be evaluated with climate models, and the potential deficiencies in these models to adequately represent the thermodynamics of the Earth system are discussed. Then, I illustrate the implications of this thermodynamic perspective by discussing the forms of renewable energy and planetary engineering that would enhance the overall free energy generation and, thereby 'empower' the future of the planet.

Life, hierarchy, and the thermodynamic machinery of planet Earth.

Throughout Earth's history, life has increased greatly in abundance, complexity, and diversity. At the same time, it has substantially altered the Earth's environment, evolving some of its variables to states further and further away from thermodynamic equilibrium. For instance, concentrations in atmospheric oxygen have increased throughout Earth's history, resulting in an increased chemical disequilibrium in the atmosphere as well as an increased redox gradient between the atmosphere and the Earth's reducing crust. These trends seem to contradict the second law of thermodynamics, which states for isolated systems that gradients and free energy are dissipated over time, resulting in a state of thermodynamic equilibrium. This seeming contradiction is resolved by considering planet Earth as a coupled, hierarchical and evolving non-equilibrium thermodynamic system that has been substantially altered by the input of free energy generated by photosynthetic life. Here, I present this hierarchical thermodynamic theory of the Earth system. I first present simple considerations to show that thermodynamic variables are driven away from a state of thermodynamic equilibrium by the transfer of power from some other process and that the resulting state of disequilibrium reflects the past net work done on the variable. This is applied to the processes of planet Earth to characterize the generation and transfer of free energy and its dissipation, from radiative gradients to temperature and chemical potential gradients that result in chemical, kinetic, and potential free energy and associated dynamics of the climate system and geochemical cycles. The maximization of power transfer among the processes within this hierarchy yields thermodynamic efficiencies much lower than the Carnot efficiency of equilibrium thermodynamics and is closely related to the proposed principle of Maximum Entropy Production (MEP). The role of life is then discussed as a photochemical process that generates substantial amounts of chemical free energy which essentially skips the limitations and inefficiencies associated with the transfer of power within the thermodynamic hierarchy of the planet. This perspective allows us to view life as being the means to transform many aspects of planet Earth to states even further away from thermodynamic equilibrium than is possible by purely abiotic means. In this perspective pockets of low-entropy life emerge from the overall trend of the Earth system to increase the entropy of the universe at the fastest possible rate. The implications of the theory are discussed regarding fundamental deficiencies in Earth system modeling, applications of the theory to reconstructions of Earth system history, and regarding the role of human activity for the future of the planet.

Maximum entropy production in environmental and ecological systems.

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.

Maximum entropy production allows a simple representation of heterogeneity in semiarid ecosystems.

Feedbacks between water use, biomass and infiltration capacity in semiarid ecosystems have been shown to lead to the spontaneous formation of vegetation patterns in a simple model. The formation of patterns permits the maintenance of larger overall biomass at low rainfall rates compared with homogeneous vegetation. This results in a bias of models run at larger scales neglecting subgrid-scale variability. In the present study, we investigate the question whether subgrid-scale heterogeneity can be parameterized as the outcome of optimal partitioning between bare soil and vegetated area. We find that a two-box model reproduces the time-averaged biomass of the patterns emerging in a 100 x 100 grid model if the vegetated fraction is optimized for maximum entropy production (MEP). This suggests that the proposed optimality-based representation of subgrid-scale heterogeneity may be generally applicable to different systems and at different scales. The implications for our understanding of self-organized behaviour and its modelling are discussed.

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

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.

Nonequilibrium 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.