Unifying ecology and climate with the fourth law of thermodynamics

Part II Biodiversity regulates climate

The idea of earth as a living and self-organizing system, where ecology and climate synergize as an organism, is an enticing one. Over the past century and a half, various pioneering researchers have been working on the story of how this could be so from a scientific perspective.

This story is one of circulation. Sunlight is absorbed by plants, turns into chemical energy and circulates through the food web. Water circulates through the ecosystem and atmosphere.

This story is one of order and disorder. The sun’s energy helps create gradients, temperature gradients and chemical gradients, that help drive the self-organization of ecology and climate. The earth inputs the sun’s order, uses it to run the planet, and outputs disorder.

This story is of the earth as a cell, with the earth’s atmosphere similar to the cell’s membrane. The cell grows its membrane. The earth grows its atmosphere (earth’s life forms release gases and water that create the atmosphere). The cell creates a proton gradient across its membrane that it uses to drive various processes essential for its functioning. The earth’s biodiversity creates a temperature gradient across the atmosphere that it uses to drive convection and the small water cycle that are essential for its functioning.

These ideas of circulation, order, disorder, entropy, energy, gradients are part of a field called nonequilibrium thermodynamics. The first three laws of thermodynamics are about equilibrium systems, as exemplified by a pot of water that is at room temperature, and about the approach to equilibrium, as exemplified by a pot of water cooling to room temperature. There is a proposed fourth law of thermodynamics which is about driven nonequilibrium systems, as exemplified by a boiling pot of water on a stove top. These driven systems can emerge new forms of order like the convective loops that form in the pot, forms that are called dissipative structures. The fourth law suggests that these systems move at maximum power, so in the case of the convective loop, it brings heat upwards at maximum power.

Applying this fourth law of thermodynamics to ecology can help enlighten how life could self-organize on earth to form biodiverse ecologies. It can clarify how life evolves the atmosphere’s temperature gradients and rain patterns to help support life.

Applying this fourth law of thermodynamics to the climate allows us arrive at accurate results for some climate scenarios, without having to use global climate models that take extensive computer simulation time. It thus has the potential to revolutionize climate science. The fourth law may allow us to quantify how biodiversity loss, land degradation and the draining of water from our continents affect extreme weather and global warming.

To understand more of this nonequilibrium, self-organizing picture of the earth, lets look back in history to see how these ideas developed.

Life and the problem of complexity

According to the second law of thermodynamics, entropy should always be increasing. If so, then why does life seem to get more complex? This was a question that Ludwig Boltzmann, who birthed the field of statistical mechanics, the foundational theory for thermodynamics, pondered in the 1870s. Boltzmann reasoned that “the general struggle for existence of animate beings is not a struggle for raw materials… but a struggle for [negative] entropy, which becomes available through the transition of energy from the hot sun to the cold earth.” He pointed to the nonequilibrium properties of heat moving from the sun to the earth as the key to how to solve the problem of why life could grow order. He died of entropy though before he could fully solve the problem.

Ernest Schroedinger, a physicist who helped found the field of quantum mechanics, came to a similar conclusion, he wrote in his famous book What is life? in 1944 that “the device by which an organism maintains itself stationary at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment.”

The secret of life, Boltzmann and Schroedinger were telling us, are to be found in understanding the picture of nonequilibrium thermodynamics.

The earth is in nonequilibrium because energy is being continuously inputted from the sun and outputted by radiation into space. The earth is inside a much bigger system, the universe, which has more room for entropy, so nonequilibrium thermodynamics states that the universe will want more of that entropy. Earth thus evolves to a state that outputs entropy at a higher rate. In so doing the earth will order itself.

Ecology and the fourth law of thermodynamics

Alfred Lotka was a bio-mathematician who came up with the famous Lotka-Volterra equations that model predator-prey relationships, equations that helped birth the field of theoretical population ecology. He was puzzled by what natural selection was selecting for. To him, and also to many others, saying natural selection selects for fitness is problematical, because it is not clear what fitness is. If we define fitness as what helps survival then we have a tautological statement that natural selection selects for those species that survive. Lotka rather proposed that natural selection selects for those organisms that evolve to process energy through its system faster. He wrote ‘the organisms that capture and use energy more rapidly and effectively have a selective advantage’ and ‘natural selection tends to make the energy flux through the system a maximum, so far as compatible with the constraints to which the system is subject.’ [1922]

He stated that in a ecosystem with plants and herbivores, over time the system will evolve so that the plants grow faster, and more food would be available for the animals. In his framework animal help plants grow faster, by pooping nutrients for the soil, and spreading plant seeds. Natural selection selects for those animals which help the plants. Ecosystems thus tends to maximal energy flow. The plant-animal system is an autocatalytic cycle where each part of it is helping catalyse the other. Plants enable more animal growth, and animals enable more plant growth.

This puts the unit of natural selection not just at the individual, but also at that of the cycle. Individuals evolve. Autocatalytic cycles also evolve.

A couple of decades later, Howard Odum, an ecologist who helped birth the field of ecosystem ecology, evolved Lotka’s ideas further. Odum was in the field measuring the flows of energies throughout the ecosystem, he was in the water looking at how algae provided nutrients to coral polyps they were nestled in. Odum became curious that many of the energy flows through the trophic levels of an ecosystem were not that efficient. This led him to work with the physicist Richard Pinkerton, to suggest that ecosystems move towards maximal power rather than maximal efficiency. They took the Maximal Power Theorem from electronics and applied it to ecology. [Odum, Pinkerton 1955]

To illustrate the idea of how systems produce maximal power lets use the example of bicycling. When you pedal on the small gear on a bike, you will be efficient because you are not losing frictional power, and your legs will be spinning fast, but the bike won’t go that fast. If you use a big gear, it is very inefficient because of frictional losses, so the bike also won’t go very fast. There is a sweet spot where you pedal at an intermediate rate and intermediate gear to get the bike to go at maximal power.

[Fig 1.]

In a mature ecosystem the rate of consumption of plants by herbivores would not be too low, because then the herbivores do not have enough energy, and the rate of consumption would not be too high because then the plants get consumed faster than they can grow back. At low rates of consumption, animals make efficient use of the food, but not much poop is created to build the soil for the plants. At high rates of consumption, there is temporarily more poop, but then that poop decreases as there are not enough plants for the animals. There is thus an intermediate rate of consumption that leads to maximal power for the system.

In 1983 Odum proposed the Maximum Power Principle : “During self-organization, system designs develop and prevail that maximize power intake, energy transformation, and those uses that reinforce production and efficiency."

An experiment to test the idea that systems maximize power intake was done by Clay Montague, Joseph Davis and Tony Cai. They set up a plankton tank, with light shining on it, where the length of time the light shone depended on the pH of the water. The plankton could adjust the pH of the water by secreting acid. The researchers wanted to see if the plankton community would evolve and naturally select over several weeks, the lifetime of a plankton being several days, for plankton that secrete the right amount of acid to keep the light shining longer. Indeed the plankton did, suggesting they evolved to maximize power intake. [Cai 2006]

Odum called the Maximum Power Principle, the fourth law of thermodynamics. There have been some other proposals for a fourth law of thermodynamics like the concept that nonequilibrium systems will move towards maximum entropy production. These proposals are closely related, since, to produce maximum entropy production probably requires maximum power production, as the system is trying redistribute energy over as wide as possible amount of states as quickly as possible.

Odum later in his life, also proposed a fifth and sixth law of thermodynamics to describe in more detail how ecosystems behave as they mature. Ecosystems have an establishment phase which favor so called r-strategists, who are pioneer species that reproduce well, and a maintenance phase which favors k-strategists who grow slowly and live close to the carrying capacity of the habitat. In their maintenance phase, a significant percentage of an ecosystem’s power goes into maintenance. [Odum 1969]

David Holmgren, co-founder of permaculture, says his biggest influences on his ideas about permaculture were Bill Mollison, his fellow permaculture co-founder, and Howard Odum. He dedicated his Permaculture book to Howard Odum, and mysteriously wrote about the Maximum Power Principle briefly in the book but didn’t elaborate further. In permaculture the concept of waste=food is closely tied to the concept of autocatalytic circles. Various permaculture like companion planting, hugelkultur, compost teas help maximize power flow through the autocatalytic cycles in the garden and farm. The problem with industrial farming is that it tries to create power through methods in ways that destroy the auto-catalytic cycles. Its operating at too far to the right on the figure 1 above. Synthetic fertilizers and pesticides disrupt, weakening the plant-soil cycle, rather than increasing its power.

I think bringing in nonequilibrium thermodynamics and the fourth law into permaculture could get it adopted by a much wider crowd who may want a more scientific basis to understanding why it should be doing the practices permaculture suggests. Howard Odum worked with agroecology to integrate his ideas into that movement, and agroecology has found a home at many universities.

Understanding how permaculture and agroecology helps maximize power in the atmosphere, will help us to understand how permaculture and agroecology can help restore the climate, something we will touch on later in this essay.

Dissipative Structures

Ilya Prigogine was a Belgian physical chemist who studied far from equilibrium systems and how they produced order. In the 1960s he described how these systems create dissipative structures; this work would win him the Nobel Prize in chemistry.

To illustrate the idea of dissipative structures, lets look at a pot of viscous liquid being heated. The liquid attempts to dissipate the heat as quickly as possible. At low levels of flame, the heat is passed upward by conduction, by liquid molecules vibrating the molecules above them, whilst the liquid as a whole remains stationary. At higher levels of flame the heat gets transferred by convection which means the liquid starts circulating. Convection can carry heat upwards faster. At even higher levels of flame these convection loops will self-organize themselves into loops which form a hexagonal structure in the liquid, called Rayleigh-Bernard cells.

Now what is the best speed for these convective loops to move at to bring up heat fastest? If they move too fast they themselves will create friction and heat. If they move slowly then heat won’t be brought up fast. So there is some intermediate speed that the convective loops move at to bring up the heat at fastest speed. This intermediate speed is the state of maximum power. The pot liquid wants to move at maximum power, because that is the fastest way to move towards a maximum entropy state.

Prigogine called these organized convective loops - dissipative structures. He postulated that whenever a system is driven far from equilibrium it will have a gradient like a temperature gradient or a chemical gradient, and that the system will attempt to reduce this gradient and in the process produce order in the form of dissipative structures.

Hurricanes, whirlpools, oscillatory enzyme processes like the Kreb’s cycle, are examples of dissipative structures. Animals are a nonequilibrium thermodynamic engine that turns food into poop. The animals’ autocatalytic cycles of molecules making and unmaking each other as they process the food, are an emergent dissipative structure.

Eric Schneider, a marine geologist, and James Kay, an ecological scientist, built on the ideas of Prigogine and Odum to try and understand life on earth. They came up with a restated second law of thermodynamics “As systems are moved away from equilibrium, they will utilize all avenues available to counter the applied gradients. As the applied gradients increase, so does the system's ability to oppose further movement from equilibrium.” They wrote that “If we view the earth as an open thermodynamic system with a large gradient impressed on it by the sun, the restated second law suggests that the system will reduce this gradient by using all physical and chemical processes available to it. We suggest that life exists on earth as another means of dissipating the solar induced gradient and as such, is a manifestation of the restated second law.” [Schneider, Kay 1995]

The ecosystem evolves to absorb more sunlight, which then allows it to generate more power by extracting more order from the photons. The photons come in an ordered form of sunlight as short wave radiation which are higher energy. It then goes back into space in more a disordered form as long wave radiation which are lower energy. The photons get beamed onto the earth in an ordered diurnal (more photons during day, less at night), and seasonal (more in summer, less in winter) pattern and then get radiated back out to space in a more spread out, higher entropy manner over days, nights, and seasons, because the soil can hold the heat from the sun for awhile before it releases it.

Schneider and Kay write “as ecosystems grow and develop, they should increase their total dissipation, develop more complex structures with more energy flow, increase their cycling activity, develop greater diversity and generate more hierarchical levels, all to abet energy degradation. Species which survive in ecosystems are those that funnel energy into their own production and reproduction and contribute to autocatalytic processes which increase the total dissipation of the ecosystem.” [Schneider Kay 1994] Schneider and Kay cite research that shows mature ecosystems end up at cooler temperatures than nearby barer landscapes, as evidence that mature ecosystems are better at degrading the incoming energy.

The small water cycle and dissipative structures

Wilhelm Ripl was an Austrian ecologist who pointed out that the earth evolved dissipative water structures. He wrote “The solar-driven, dissipative water and matter cycles—with water as the most important dynamic agent—have shaped the face of our planet Earth and constitute the key for life. The various energetic properties of water to dissipate energy as, for example, the cyclic processes of evaporation and precipitation, of dissolution and crystallization, and finally—water in the biological cell—of disintegration of the water molecule and recombination of water (carbon fixation and respiration), coupled in a recursive way, are together the three most essential cyclic water processes damping the solar pulse. [Ripl 2003]

Plants, animals, fungi, and bacteria need water. From a nonequilibirium thermodynamic perspective, if the autocatalytic cycles of the ecosystem need more water at certain times to run with more power, then there is a tendency for the system to evolve ways to increase the water supply when needed. In the case of the earth there are two water cycles it can regulate to bring water to the plants, i) the small water cycle - where plants and soil evapotranspire water from the land that then turns into rain, and ii) a lower water cycle, where tree roots pump water to the aquifers during wet season and then draw that water up again during dry season in a process called hydraulic redistribution.

To increase the small water cycle there are many things plants, animals, fungi and bacteria can do. They can slow and absorb more of the rain in the landscape which allows more water to become available for evapotranspiration. Fungi, bacteria, plants and animals can build up the organic content in soil so it absorbs more rain. Fungi can release spores into the air that seed rain. Animals can spread seeds which turn into vegetation that slows water, they can dig earthworks that slow water, and they can create dams in streams that cause the water to overflow into the landscape. More biodiversity enables more ways to increase the small water cycle.

Ripl explains that as ecosystems and climate mature they will shift to more localized water cycles for better management. He writes that as the earth evolved “open systems turned into more closed and stable systems owing to more resource-economic adaptations to local and phase-related behaviour. These better optimized structures could grow and spread, whereas less efficient processes with more open structures and higher losses were forced to shrink….the most crucial stabilizing process is the short-circuited water cycle—between evapotranspiration and precipitation. To a large extent this process already takes place under and within the tree canopy. The control of local material flow takes place mainly within biota. Locally, water cycles that are more completely closed—in part internalized within organisms and ecosystem structures—are thus controlling localized, short-circuited, matter management.”

As the earth evolves to absorb more sunlight through plants multiplying, there becomes a larger energy gradient on earth, and so dissipative structures like the small water cycle and lower water cycle can evolve to grow in size. Vegetation in general bring more rain. If our continents were to be totally covered with vegetation there would be fifty percent more rain than if the land was all bare. [Kleidon 2000]. According to Ripl this rain will come in the form of more and more localized small water cycles as the ecosystem matures.

The small water cycle, temperature gradients, and earth as a cell with a membrane

If you have a forest or a grassland, how do you know how much of the water in the landscape will get evaporated? Axel Kleidon, a German physicist turned climate scientist, who works at the Max Planck Institute, found if there is enough water in the landscape, that the small water cycle evolves to a value near its maximum strength. The temperature difference between the earth and sky determines how much water will get evapotranspired, as it drives the upward convection of water and air. This temperature gradient lessens as convection happens because the surface of the earth cools as water evapotranspires, and the sky warms as water condenses to form clouds. A smaller temperature gradient means convection then lessens, and less water is able to be transported up. There is thus a maximum of water that can flow through the small water cycle. [Kleidon, Renner 2013]

This temperature gradient picture of the atmosphere is reminiscent of the proton gradient process in a cell. A cell creates a membrane and then it puts a proton gradient across it. That gradient then enables the flow of protons to create ATP, an energy source. The gradient depletes in the process. In a similar way the earth constructs the temperature gradient of the atmosphere, so it can use it to pump water, to enable the ecosystem to have more energy. As water flows it depletes the temperature gradient. We can think of the earth as a kind of cell with a membrane.

Over the course of evolution the earth has many ways to tune the temperature gradient, it can increase vegetation, change the albedo of the vegetation, alter the heat capacity of the soil, sequester or release carbon, distribute water more or less widely over continents, alter the amount of bioaerosols released into the air to create clouds, and change the amount of evapotranspiration. Nonequilibrium thermodynamics suggests that the earth tunes the temperature gradient to a value that allows the planetary system to operate at maximum power.

We can do calculations for the proton gradient of a cell. We can also do calculations for the small water cycle of the atmosphere, and get numbers that reflect observed measurements. Kleidon and Renner used maximal arguments to explain observed values in the diurnal variation of sensible heat (the vibrational motion of the air) and latent heat (which is the heat the water vapor carries) ratio for different ecosystems [(Kleidon and Renner 2018]. One reviewer on looking at their results said they got better answers than global climate models.

Climate, maximal states, and the fourth law of thermodynamics

This maximal thermodynamic approach to climate was first pointed out by Edward Lorenz, one of the fathers of chaos theory, when he observed that the atmosphere tends towards states of most intensity, given constraints. The approach has since been developed by many researchers to obtain as good results as global climate models get. Some calculations for which this has been done is for how heat moves from the equator towards the poles through the atmosphere [Paltridge 1978], for how the water cycle responds to the global warming [Kleidon], for calculating the difference in climate sensitivity between land and ocean (Kleidon and Renner 2017], and, for calculating the temperature and rainfall loss that happens when forests are cut down in the Amazon [Conte, Kleidon 2019].

Thermodynamics explains that we do not need to know all the motions of the atoms in order to get a macroscopic understanding of how a system would behave. With the help of the three laws of thermodynamics one is able to make accurate calculations about the behavior of a system. Nonequilibrium thermodynamics applies to climate science. For numerous climate scenarios we do not necessarily need to know all the detailed information of how the air is moving that goes into many global climate models, in order to get accurate calculations of the atmosphere’s behavior. With the newer (and not yet fully established) fourth law of thermodynamics, we can get an understanding of why the climate emerges certain behaviors. We can using this approach get an equation for how the climate responds to climate drivers, in contrast to global climate models which can only give us simulation results. By putting ecology and climate on the same theoretical foundation we can quantify how they will couple without knowing all the details, because we know they will evolve to certain maximal states. My guess is that nonequilibrium thermodynamics, dissipative structures, and the fourth law of thermodynamics will revolutionize climate science in the upcoming years. They will become a respected tool alongside global climate models.

One area I see the fourth law of thermodynamics helping us understand is that of the importance of teleconnections - how deforestration or paving over of the land on one continent can impact the weather on another. Recent global climate models have shown how deforestration on continent influences large scale atmospheric circulations like the Hadley cell, which can then impact the jet stream, and cause it to buckle. When jet streams buckle it can lead to extreme weather events in places all over the world, like the huge snowstorm that hit Texas in 2022.

The Hadley cell and the jet stream can be described by the maximal power state they attain. If we affect the landscape hydration levels in one continent, it will affect the maximal power state of the jet stream, which will impact the number of extreme weather events in the world. Landscape hydration can be negatively affected by anthropogenic changes like deforestration, the paving over of the land, the building of roads, and the construction of sewage systems that funnel water out of the landscape. Land hydration can be positively affected by beavers, biodiversity, wetlands regeneration, soil organic content increase, and various permaculture and agroecology methodologies. Possibly we can derive an equation for how landscape hydration changes impacts extreme weather using maximal arguments. If we then quantify how anthropogenic changes affects land hydration, we will have a determination for how land use anthropogenic changes affect extreme weather.

One of the reasons the ‘carbon impacts climate’ story grew much bigger than the ‘land use, water and biodiversity impacts climate’ story, even though both are important, is that the carbon story was more easily quantifiable. By giving us the tools to quantify how land use, water and biodiversity impact climate, nonequilibrium thermodynamics may become a useful tool in the future for the climate movement.

The self-organizing, complex systems, nonequilibrium thermodynamic view of ecology and climate has been slowly emerging over the past century and a half, brought forth by a band of pioneers, many of which have helped birth their own fields of science, Boltzmann with statistical mechanics, Schroedinger with quantum mechanics, Lotka with population ecology, Odum with ecosystem ecology, and Lorenz with chaos theory. Theirs and others research form an extraordinary body of work that sheds light on how biodiversity creates, couples and co-evolves with the climate, and how the earth regulates itself through its atmospheric membrane. It illuminates why nature does so much better than man-made infrastructure to run the planet.

Nonequilibrium thermodynamics might also be able to show us a path for how to align our economy with ecology, as the fourth law also applies to economics [Odum 2007]. Using this formulation we might be able to develop a paradigm where economics is a subset of ecology. There may be ways of using maximal power instead of GDP as a measure of economic health, and in so doing point a way forward where biodiversity increases the economy, and increasing the economy restores the climate.

Nonequilibrium thermodynamics is a nascent science that will bring many more important insights about the deep workings of our planet in the future.

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Whoah thats a lot of information covered in this essay, you might want to read it a couple of times, and chew on the ideas a bit. This stuff has many implications. Its still an emergent science with multiple people coming at it from multiple perspectives, so the whole story is not fully ready to be told yet. There’s youtube videos of Axel Kleidon and Howard Odum that might help you understand more of this content, and go into with more depth.

This essay follows a previous essay. Here is part I : Biodiversity regulates climate. Adventures in Daisyworld.

This is a reader supported publication, please consider supporting financially if you have the means.

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