Submitted:
07 January 2026
Posted:
08 January 2026
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Abstract
Keywords:
1. Introduction
2. Materials and Methods
2.1. Brief Introduction to the Concept of “Entropy as a Criterion for Sustainability” and Its Application to CDR Technologies
2.1.1. Entropy as a Criterion for Sustainability
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- Sustainability comprises the whole biosphere, not only the climate, i.e., it concerns the whole biosphere and not only humans and their (relatively short-term) needs but also all members and components of ecosystems as humans live from what the earth can sustainably produce (including but by far not only pure water, fresh clean air, and fertile soil). (This understanding of sustainability is far from what ecocentrism is promoting.)
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- A certain product or process A can be called “more sustainable” than alternative B, if A produces less entropy, entropy in any form.
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- Entropy is a quantitative indicator for any kind of (utility) value loss in energy, matter or functional complexity. Insofar, it is a general sustainability indicator that does not specifically tell us whether losses are for example caused by the transformation of primary energy (such as coal) into electricity (thereby generating also lower value energy in the form of heat and low value matter in the form of ash); or whether electricity used for air conditioning results in a lower level of energy value; or whether the entropy increase indicates value loss by intoxification of ground or coastal waters leading to serious degradation of ecosystems.
2.1.2. Sustainability Analysis of CDR Technologies with the Entropy Criterion
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- CO2 emission and dilution in the atmosphere are understood as a process leading toward thermodynamic equilibrium, i.e., accompanied by increasing entropy (in the atmosphere: the entropy of mixing); the same is true for any pollution of rivers, ground or coastal waters, and soil erosion in agriculture with loss of nutrients and humus into the seas: processes toward equilibrium with increasing entropy; this is also the case with the formation and distribution of microplastic, abrasion or corrosion products and any degradation of functioning complexity, such as ecological networks, and a decrease in biodiversity: entropy increases toward equilibrium. CDR requires an overcritical amount of energy accompanied by a decrease in entropy of the atmosphere and orders of magnitude greater increase in entropy of the Earth’s surface.
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- The newly proposed concept of “entropy as a criterion for sustainability” allows the quantitative evaluation of the degree of sustainability of products and processes. Entropy is a useful physical quantity for objectively and falsifiably judging sustainability, comparing different processes or products with respect to their degree of (non)sustainability. Life is a “dissipative structure” (or process) with minimum entropy created in nonequilibrium far from equilibrium, “equilibrium is death”6. To technologically maintain functioning nonequilibrium systems, constant overcritical energy influx and energy-consuming work are needed. The increase in entropy accompanied by these processes will accumulate on Earth as waste, pollution, complexity decay and losses if it (the entropy) cannot be emitted as infrared radiation into space (cf. below).
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- Energy demand and entropy increase analysis reveals that CDR technologies are far from sustainable; in fact, collateral environmental damage will be orders of magnitude greater than the positive effect in mitigating climate change.
2.2. Preservation of Biodiversity Plus Natural CO2 Capture and Storage Mechanisms in Ecosystems (with a Focus on Bioagriculture)
2.2.1. Sustainability of Natural Processes from an Entropy Standpoint of View
2.2.2. Biodiversity Improvement and CDR Contribution by Organic Farming
2.2.3. Crop Rotation
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- 5% of the cropland (15 hectares in this study) to be planted with a diverse mixture of flowers, which remain in place from May 15 to mid-February of the following year and actively promote insect populations while also providing a good shelter and food source for birds in winter.
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- Each field was divided into at least three smaller fields, with no area smaller than 2 hectares and no area larger than 5 hectares. In their largest field (over 50 hectares), there are 11 different fields and three flower strips.
2.2.4. Carbon Storage in Soils - Mechanism
2.2.5. Methane Emission Issues Associated with Milk Production vs. CO2 Storage while Grazing
2.2.6. Organic Farming and Carbon Content in Soil
3. Results
4. Discussion
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- Conventional farms have socialized the cost of environmental pollution caused by them (such as increased water cleaning to remove fertilizer and other toxic residues from ground and surface waters or to combat algae blooms), not to address the unknown future costs of species decline caused by pesticides.
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- The Kattendorf organic farm (like several others) creates added value for society and ecology, which it is not paid for. The ecological added value for increased biodiversity cannot be quantified, but CO2 fixation and storage of 3404 tons of CO2 per year would be worth approximately 250.000 € if the EU emission trading course (73 €/t) were taken as of July 30, 2025 [45]. If the CCS or DAC costs for CO2 removal would be taken, the value would be in the range of 1.7 million Euro [46], and even if the costs as hoped for DAC (150 €/t) would be worth half a million Euro.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
| 1 | For an overview describing the various meanings of “sustainability” cf https://en.wikipedia.org/wiki/Sustainability
|
| 2 | Its definition is dS = dQ/T, with dS being change in entropy, dQ the change in heat per temperature T. For chemical reactions it is dG = dH – TdS [or: dS = (dH – dG)/T], i.e.: entropy change is the difference of reaction enthalpy and free energy change divided by temperature. Boltzman’s formula S = k*lnP (k being the "Boltzman constant“, P the probability) is just one interpretation of entropy. |
| 3 | The amount of erosion, i.e., loss of potentially fertile soil, even in flat regions amounts to almost 2 mm/year equivalent to 22.5 +/- 7.2 metric tons per hectare and year for conventionally farmed land, which are in total 57.6 × 109 +/- 37.8 × 109 tons over the past 150 years in the study area in Midwestern US [9]a). Soil erosion is much less on biologically farmed land (approximately 0.2 tons per hectare and year, compared to 22.5 tons per hectare and year) depending on the farming practice, especially whether or not land is covered with plants all year round [9]b). |
| 4 | It can not be an excuse to argue one does not plan to use CO2 as raw material for all and any organic chemical actually in use in the chemical industry and beyond it, but "only“ for very well selected ones. The calculation shows that any CCU project is even more unsustainable than already DAC alone which is true for any small or large scale. |
| 5 | |
| 6 | Ludwig von Bertalanffy, the creator of the "steady state“ ("Fliessgleichgewicht“) theory, wrote: "Biologically, life is not maintenance or restoration of equilibrium but is essentially maintenance of disequilibria [i.e.: "nonequilibrium“ in the sense of Prigogine’s theory, BW], as the doctrine of the organism as open system reveals. Reaching equilibrium means death and consequent decay.” [16] |
| 7 | |
| 8 | "Kattendorfer Hof“, https://www.kattendorfer-hof.de
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| 9 | This is a form of direct marketing in which the individual consumers are booking a share of the farm’s crops harvest and products, so that the farm does not at all or only partially sell products to dairiesor wholesale trading comanies, cf. https://en.wikipedia.org/wiki/Community-supported_agriculture. |
| 10 | German: "Gesellschaft bürgerlichen Rechts“, GbR |
| 11 | GmbH & Co. KG, "KG“ (= Kommanditgesellschaft, a personal partnership with limited personal liability) in combination with the GmbH (= "Inc.“) as the "personally“ liable partner, which itself is a limited liability partnership |
| 12 | The GmbH is owned by shareholders who are partners in both KGs. |
| 13 | Conventional farming does not prefer to have wall hedges as they make farming more work-intensive due to the fields being smaller, and due to loss of "productive“ area. In the case of the Kattendorf farm, the 12.51 km wall hedges correspond to approximately 2.5 to 3 hectares which conventionally would be judged as "unproductive“ or even "counterproductive“, but they are very productive in terms of biodiversity and prevention of soil erosion by wind. |
| 14 | Also fast-growing forests for conversion of the wood into heat, electricity, fuels and catch the emitted CO2 again with CCS technology, or fast growing macroalgae farms are "en vogue“, we will take a critical look at these in section 4 "Discussion“. |
| 15 | cf. chapter 8, p. 260 ff [11] |
| 16 | |
| 17 | 365 days x 700 l/day x 0.6443 g/l CH4 = 165 kg/cow, year; the value 0.6443 was calculated using wolframalpha’s web site: https://www.wolframalpha.com/input/?i=mass+of+1+l+methane+at+300+K+and+1+bar
|
| 18 | |
| 19 | in total 50 milk cows plus 15 nurse cows, and approximately 150 heads cattle/calves |
| 20 | As the Kattendorf farm is not a limited and small experimental project or an object of research for an external research institute but a real-life and relatively big economic undertaking, there is no capacity to completely quantitively investigate and document the species diversity and density over 450 hectares leased land having such a highly differentiated and dynamic plant coverage. Therefore, the very obvious differences to the neighboring conventional fields can be mentioned as well as selected detailed observations (made by 4 of the shareholders: 1 biologist (insects, birs), 1 hobby ornithologist, 2 M. A. vegetable farmers). A neighbor, who since more than 20 years lives in the very small village (5 houses) right besides the 240 hectares leased farmland, said: "Here is much more bird life since you are renting this land.“ The lease of fields at the 2nd location started 2018 with first 80 hectares and 2020 with the remaining 160 hectares, then starting to convert the fields from conventional, very intensive corn farming to organic farming. |
| 21 | in addition to the farm’s own wood from wall hedges which are counted with Zero CO2 emissions |
| 22 | Only the cereals are sold to a relatively big biobakery which in return also supplies bread to the farm’s shops, but sells much more bread to many other shops in North Germany. |
| 23 | The wording "survival“ is used on purpose (instead of "success“) as during the 30 years of existence, only a few years had been appropriately profitable, mostly the profit was minimal and just sufficient to survive. In light of low food prices for conventional food and increasingly also for (sometimes only "so-called“) biofood in supermarkets, it is very hard for the Kattendorf farm to survive in spite of its business model. After Russia’s invasion of Ukraine and the following increase of the inflation rate (leading to a strong shift of the biofood market to the 4 biggest supermarket chains in Germany with 85% of the market share and to specialized biofood-supermarket chains), sales have decreased by approximately 20%, many other smaller organic food stores have experienced the same and closed, the farm’s own shops thus far have survived but may need to become restructured; it helped that sales have somewhat recovered in 2024 so that sales are now only 10% below sales in 2020/2021. Also the farms’ CSA organization has lost approximately 15% of its members. |
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| Yearly CO2 emissions / fixation-storage balance | min/max t CO2(eq) |
Remarks |
|---|---|---|
| Emissions | (460) | total |
| CO2eq (enteric methane) | 269 | 155 cows/cattle with 54 kg CO2eq/yr, 50 calves with 25 kg CO2eq/yr |
| fossil gas (remaining demand21) and electricity (remaining demand) | 45 | With 0,2 kg CO2 for fossil gas kWh, 0,363 kg CO2 for external current/German mix [47] |
| diesel (tractors, combine harvester, and trucks for logistics) | 146 | In total approximately 55,000 Liters diesel with 2,65 kg CO2 per liter |
| CO2 fixation/in-soil-storage | (1393/3864) | Total |
| pastures | 870/1560 | 6,7/12 t CO2, resp., per hectare |
| fields | 523/2304 | 60% of pastures’ potential |
| Result | 933/3404* | Total CO2 fixation/in-soil-storage minus emissions |
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