Submitted:
05 August 2025
Posted:
07 August 2025
Read the latest preprint version here
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
2.1.2. Sustainability Analysis of CDR Technologies with the Entropy Criterion
2.2. Preservation of Biodiversity Plus Natural CO2 Capture and Storage Mechanisms in Ecosystems (with Focus on Bio-Agriculture)
2.2.1. Sustainability of Natural Processes from Entropy Standpoint of View
2.2.2. Biodiversity Improvement and CDR Contribution by Organic Farming
2.2.3. Crop Rotation
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
| 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 CH4/yr, 50 calves with 25 kg CH4/yr |
| fossil gas (remaining demand17) 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 |
| *equivalent to savings of 6617 MWh (if captured by DAC) (at least 7*106 kJ per ton CO2 captured by DAC = 1,944 MWh/t CO2 and with 1 kJ = 0,000277 kWh), the farm itself consumes 160 MWh (PV and from grid) + 540 MWh (Diesel) + 80 MWh fossil gas and wood from wall hedges = 780 MWh (11% savings), resulting in net savings of more than 5000 MWh of energy, equivalent to an estimated primary energy amount of 14 GWh or 50 000 GJ. | ||
4. Discussion
5. Conclusions
Data availability
Ethics approval and consent to participate
Informed consent and consent for publication
Competing interest
Author details
Funding
Author contributions
Acknowledgments
References
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| 1 | 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 enrgy change divided by temperature. Boltzman’s formula S = k*lnP (k being the "Boltzman constant“, P the probability) is just one interpretation of entropy. |
| 2 | 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). |
| 3 | 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. |
| 4 | 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] |
| 5 | “Kattendorfer Hof”, https://www.kattendorfer-hof.de
|
| 6 | 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. |
| 7 | German: "Gesellschaft bürgerlichen Rechts“, GbR |
| 8 | 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 |
| 9 | The GmbH is owned by shareholders who are partners in both KGs. |
| 10 | 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. |
| 11 | 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“. |
| 12 | cf. chapter 8 in [11], p. 260 ff |
| 13 | |
| 14 | 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
|
| 15 | in total 50 milk cows plus 15 nurse cows, and approximately 150 heads cattle/calves |
| 16 | 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. |
| 17 | in addition to the farm’s own wood from wall hedges which are counted with Zero CO2 emissions |
| 18 | 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. |
| 19 | 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, 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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