by Judith Curry
Albert Einstein on thermodynamics:
A theory is more impressive the greater the simplicity of its premises, the more different are the kinds of things it relates, and the more extended its range of applicability. Therefore, the deep impression which classical thermodynamics made on me. It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.
Nonequilibrium thermodynamics and maximum entropy production in the Earth system: Applications and implications
Axel Kleidon
Abstract 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.
Naturwissenschaften (2009) 96:653–677 DOI 10.1007/s00114-009-0509-x [link to full paper].
This is the best paper that I’ve come across that clearly explains nonequlibrium thermodynamics and maximum entropy production with application to the climate system. The paper can probably be understood by anyone with an undergraduate degree in engineering, physics or chemistry. Its a long and complex paper, I will try to do it justice with some excerpts from the background and then cutting to the part that interested me most, on feedbacks:
Introduction
The parts of thermodynamics that we are usually most familiar with deal with equilibrium systems, systems that maintain a state of thermodynamic equilibrium (TE) and that are isolated, that is, they do not exchange energy or matter with their surroundings. In contrast, the Earth is a thermodynamic system for which the exchange of energy with space is essential. Earth system processes are fueled by absorption of incoming sunlight. Sunlight heats the ground, causes atmospheric motion, is being utilized by photosynthesis, and ultimately is emitted back into space as terrestrial radiation at a wavelength much longer than the incoming solar radiation. Without the radiative exchanges across the Earth–space boundary, not much would happen on Earth and the Earth would rest in a state of TE.
Systems that are maintained far from TE dissipate energy, resulting in entropy production.
Background
The first and second laws of thermodynamics provide fundamental constraints on any process that occurs in nature. While the first law essentially states the conservation of energy, the second law makes a specific statement on the direction into which processes are likely to proceed. It states that the entropy of an isolated system, i.e., a system that does not exchange energy or mass with its surroundings, can only increase, or, in other words, that free energy and gradients are depleted in time.
In the absence of external exchange fluxes, gradients would be dissipated in time, and hence, entropy production would diminish in time, reaching a state of TE. To sustain gradients and dissipative activity within the system, exchange fluxes with the surroundings are essential.
A steady state of a system is reached when the entropy change averaged over sufficiently long time vanishes
The proposed principle of MEP states that, if there are sufficient degrees of freedom within the system, it will adopt a steady state at which entropy production by irreversible processes is maximized. While MEP has been proposed for concrete examples, in particular, poleward transport of heat in the climate system, entropy production in steady state is a very general property of nonequilibrium thermodynamics, so that MEP should be applicable to a wide variety of nonequilibrium systems.
MEP and feedbacks
One of the most important implications of MEP is that it implies that the associated thermodynamic processes react to perturbations with negative feedbacks in the steady state behavior. This follows directly from the maximization of entropy production, which essentially corresponds to the maximization of the work done and the free energy dissipated by a process, as explained above. Imagine that a thermodynamic flux at MEP is perturbed and temporarily reduced. This reduction in flux would result in a build-up of the thermodynamic force, e.g., temperature gradient in the case of poleward heat transport. In this case, the process would not generate as much kinetic energy as possible. The enhanced temperature gradient would then act to enhance the generation of kinetic energy, and thereby the flux, thus bringing it back to its optimal value and the MEP state. If the boundary conditions shape the optimum change, then a perturbation of the state would be amplified until the new optimum is reached, which could be interpreted as a positive feedback to the perturbation.
What MEP states is that the functional relationship itself takes a shape that maximizes entropy production and thereby results in negative feedbacks. This maximization can be understood as the direct consequence of the system to achieve its most probable configuration of states, as in the case of equilibrium statistical mechanics.
This discussion of feedbacks and MEP is quite different from the conventional treatment of feedbacks in climatology, which are usually based on temperature sensitivities. In the usual analysis, the total change in temperature ΔTtotal is expressed as the sum of the direct response of temperature to the change in external forcing (ΔT0) and the contribution of feedbacks (ΔTfeedbacks): ΔTtotal = ΔT0 + ΔTfeedbacks.
If the total change in temperature is expressed as ΔTtotal = f · ΔT0, with f being the feedback factor, then a positive feedback is defined as f > 1, while a negative feedback is defined as f < 1. The feedback framework plays a very important role in the analysis of anthropogenic climatic change.
In principle, one could develop a similar feedback framework using entropy production rather than temperature as the central metric under considera-tion. The change in entropy production Δσtotal would then be expressed as the sum of the changes due to the external forcings and due to feedbacks: Δσtotal = Δσ0 + Δσfeedbacks, or Δσtotal = f · Δσ0. In steady state, MEP would be associated with f < 1, i.e., a negative feedback as discussed above. In case of changes in the external forcing, these would result in a change in the boundary conditions while the feedback would be associated with the change in internal configuration of the flux and gradients. With a change in external forcing, the tendency of systems to maximize entropy production would then state that, after the change, the feedback factor would initially be f > 1. That is, a small change in the flux would be amplified since the flux is no longer at the MEP state. This tendency would continue up to the point when the flux again reached the optimum value, at which point the feedback factor would change to values of f ≤ 1. This points out that optimality is a strong nonlinear aspect that is unlikely to be adequately treated in a linearized feedback framework. However, more work needs to be done to place MEP and optimality into the common feedback framework.
MEP and Earth system evolution
However, the Earth system has changed dramatically in the past. The early Earth very likely had an atmosphere with a high carbon dioxide concentration and in which free oxygen was basically absent. Over time, carbon dioxide was removed to trace-gas amounts, while oxygen increased substantially during the great oxidation event some 2.3 billion years ago, and again about 0.5 billion years ago, to near current levels. So how can nonequilibrium thermodynamics inform us about how the evolution of the Earth system has proceeded in the past?
Kleidon (2009) proposes that the Earth system over time has evolved further away from the planetary TE state towards states of higher entropy production, and suggests that this overarching trend can be used to drive how the Earth’s environment has changed through time. Central here is that the reference states of TE with respect to motion and fluxes of water and carbon, as described in the section “Entropy production by earth system processes” above, are interconnected. TE at the planetary scale would be associated with the absence of large-scale motion,since only in the absence of motion would there be no frictional dissipation, hence, no entropy production by motion. Such a state of an atmosphere at rest would be saturated with water vapor since atmospheric mo- tion acts to dehumidify the atmosphere. A saturated atmosphere in turn would likely be associated with high cloud cover and no net exchange of moisture between the surface and the atmosphere. This implies that there is no continental runoff, and no associated cycling of rock-derived, geochemical elements. For the geologic carbon cycle, this implies no carbon sink, so that the atmospheric carbon dioxide concentration would be high, in turn resulting in a strong greenhouse effect and high surface temperatures. High surface temperatures would result in ice- and snow-free conditions. Overall, because of the high cloud cover, absorption of solar radiation would be low, as would be planetary entropy production. While it is unlikely that the Earth actually ever was in a state of TE, what is shown in Table 1 nevertheless provides an association of what the Earth’s environment should look like closer and further away from a state of planetary TE.
A basic positive feedback between the water, carbon, and atmospheric dynamics was also postulated to be modulated by life: Stronger atmospheric dynamics (“motion”) would result in an atmosphere in which the hydrologic variables would be maintained further away from TE, which would imply a drier atmosphere, higher fluxes of precipitation and evapotranspiration, higher ocean–land transport, etc. This in turn would drive the geologic carbon cycle to lower carbon dioxide concentrations, resulting in a weaker greenhouse effect, which in turn would cool the Earth. A cooler Earth could maintain more extensive snow and ice cover, thus enhancing the radiative forcing gradient between the tropics and the poles. This, in turn, would strengthen the atmospheric dynamics and close the positive feedback loop.
This positive feedback would cause fundamental, thermodynamic thresholds in the whole Earth system. These thresholds would imply that planetary entropy production would unlikely increase continuously during the evolution of the Earth system, but in a step- wise fashion. Once such a thermodynamic threshold is reached, the positive feedback would cause the Earth system to rapidly evolve to a state of higher entropy production, after which the system would be maintained in a stable, MEP state.
These climatic trends associated with how far the Earth system is maintained away from TE at the planetary level could help us to better reconstruct and understand the past evolution of the Earth system. This would, however, need to be further evaluated, e.g., with more detailed simulation models that explicitly consider the nonequilibrium thermodynamic nature of Earth system processes.
Summary and Conclusions
At the same time, a more solid foundation of MEP is needed. Once this foundation is successfully established, it implies that the dynamical description of complex systems far from TE follow from the maximization of entropy production. This would have quite far-reaching implications for how we model the Earth system and understand Earth system change. It will provide us with a fundamental approach to understand the success of optimality approaches that have previously been used to understand complex systems. Nonequilibrium thermodynamic measures such as entropy production may also be a more useful property to express climate sensitivity than the conventional temperature measures, as it is closely associated with the dissipative activity of the process under consideration.
In conclusion, nonequilibrium thermodynamics and MEP show great promise in allowing us to formulate a quantifiable, holistic perspective of the Earth system at a fundamental level. This perspective would allow us to understand how the Earth system organizes itself in its functioning, how it reacts to change, and how it has evolved through time. Further studies are needed to better establish the nonequilibrium thermodynamic basis of many Earth system processes, which can then serve as test cases for demonstrating the applicability and implications of MEP.
JC comments: The 2nd law of thermodynamics is an underutilized piece of physics in climate science. It is not a simple beast to wrestle with, but I think there are some important insights to gain. Optimality, self-organizing criticality, and nonlinearity are factors that are not adequately accounted for in traditional climate feedback analyses, and an entropy-based framework would be more consistent with the climate shifts that are actually observed.
With regards to the previous too big to know post, it is this kind of analysis and conceptual framework that is needed to advance our understanding, an idea that provides a blueprint for assembling the bricks into a structure.