Investigating the Health of a Rice Field Ecosystem Using Thermodynamic Extremal Principles


  • Ayan Mondal The University of Burdwan
  • Nilanjan Das The University of Burdwan
  • Rituparna Banerjee The University of Burdwan
  • Sunanda Batabyal The University of Burdwan
  • Sohini Gangopadhyay The University of Burdwan
  • Harisankar Ray The University of Burdwan
  • Nivedita Biswas The University of Burdwan
  • Sudipto Mandal The University of Burdwan



Far-from-equilibrium system; Goal-function; Rice field ecosystem; Thermodynamic ecology


This study investigates the dynamic behaviour of a rice field ecosystem and aims to define its integral features using the stability concept of an ecological goal function. This function is based on the extremal principles of thermodynamics, which assume that certain energetic processes of ecosystems—such as the rate of exergy destruction—are directed by the self-organizing informatics of the systems towards maxima or minima. 

In our study, we exploit the availability of substantially long time-series data relating to a rice field ecosystem to gain an evocative understanding of its growth trajectory in light of the thermodynamic principles. We accomplished this by constructing a model based on the STELLA 9.0 software and calculating the extremal values of growth rates (storage) and those of exergy destruction and entropy creation. The results showed that the values of both maximum dissipation and maximum exergy progressed apace with that of maximum storage till the maturation of rice and became stable thereafter, whereas maximum residence time and maximum specific dissipation values initially decreased before their asymptotic rise. A similar pattern was also observed for the maximum specific exergy. However, the maximum power dissipation curve followed a highly fluctuated course before becoming stable on the maturation of rice.


Download data is not yet available.


Metrics Loading ...


Aoki, Ichiro, and Takahisa Mizushima. "Biomass diversity and stability of food webs in aquatic ecosystems." Ecological research 16, no. 1 (2001): 65-71.

Aoki, Ichiro. "Entropy flow and entropy production in the human body in basal conditions." Journal of theoretical biology 141, no. 1 (1989): 11-21.

Aoki, Ichiro. "Entropy laws in ecological networks at steady state." Ecological modelling 42, no. 3-4 (1988): 289-303.

Aoki, Ichiro. "Min-Max principle of entropy production with time in aquatic communities." Ecological Complexity 3, no. 1 (2006): 56-63.

Baird, Daniel, and Robert E. Ulanowicz. "The seasonal dynamics of the Chesapeake Bay ecosystem." Ecological monographs 59, no. 4 (1989): 329-364.

Bastianoni, Simone, and Nadia Marchettini. "Emergy/exergy ratio as a measure of the level of organization of systems." Ecological Modelling 99, no. 1 (1997): 33-40.

Bastianoni, Simone, and Nadia Marchettini. "Emergy/exergy ratio as a measure of the level of organization of systems." Ecological Modelling 99, no. 1 (1997): 33-40.

Bejan, Adrian, and Sylvie Lorente. "The constructal law of design and evolution in nature." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (2010): 1335-1347.

Bendoricchio, G., and Sven E. Jørgensen. "Exergy as goal function of ecosystems dynamic." Ecological modelling 102, no. 1 (1997): 5-15.

Brooks, D. R., and E. O. Wiley. "Evolution as Entropy: Toward a Unified Theory of Biology. Chicago: Univ." (1986).

Brown, James H., Pablo A. Marquet, and Mark L. Taper. "Evolution of body size: consequences of an energetic definition of fitness." The American Naturalist 142, no. 4 (1993): 573-584.

Brown, Mark Theodore, and T. R. McClanahan. "Emergy analysis perspectives of Thailand and Mekong River dam proposals." Ecological Modelling 91, no. 1-3 (1996): 105-130.

Bruers, Stijn. "A discussion on maximum entropy production and information theory." Journal of Physics A: Mathematical and Theoretical 40, no. 27 (2007): 7441.

Cheslak, E. F., and V. A. Lamara. "The residence time of energy as a measure of ecological organization, Energy and Ecological Modelling, ed. by Mitsch WJ, Bosserman RW and Klopatek JM." (1981): 591-600.

Chowdhury, Tamal, Hemal Chowdhury, Ashfaq Ahmed, Young-Kwon Park, Piyal Chowdhury, Nazia Hossain, and Sadiq M. Sait. "Energy, exergy, and sustainability analyses of the agricultural sector in Bangladesh." Sustainability 12, no. 11 (2020): 4447.

Christensen, Villy, and Daniel Pauly. "ECOPATH II—a software for balancing steady-state ecosystem models and calculating network characteristics." Ecological modelling 61, no. 3-4 (1992): 169-185.

Corning, Peter A., and Stephen Jay Kline. "Thermodynamics, information and life revisited, Part I:‘To be or entropy’." Systems Research and Behavioral Science: The Official Journal of the International Federation for Systems Research 15, no. 4 (1998): 273-295.

DeLong, John P. "Experimental demonstration of a ‘rate–size’trade-off governing body size optimization." Evolutionary Ecology Research 14, no. 3 (2012): 343-352.

DeLong, John P. "The maximum power principle predicts the outcomes of two‐species competition experiments." Oikos 117, no. 9 (2008): 1329-1336.

Dewar, R. C. "Maximum entropy production and the fluctuation theorem. " Journal of Physics A: Mathematical and General 38(2005): 371-381.

Dewar, Roderick C. "Maximum entropy production and plant optimization theories." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (2010): 1429-1435.

Dewar, Roderick C. "Maximum entropy production as an inference algorithm that translates physical assumptions into macroscopic predictions: Don’t shoot the messenger." Entropy 11, no. 4 (2009): 931-944.

Dewar, Roderick. "Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states." Journal of Physics A: Mathematical and General 36, no. 3 (2003): 631.

Fath, Brian D., and Bernard C. Patten. "Review of the foundations of network environ analysis." Ecosystems 2, no. 2 (1999): 167-179.

Fath, Brian D., Bernard C. Patten, and Jae S. Choi. "Complementarity of ecological goal functions." Journal of theoretical biology 208, no. 4 (2001): 493-506.

Frissel, M. J. "The definition of residence times in ecological models." Ecological Bulletins (1981): 117-122.

Glansdorff, Paul, and Ilya Prigogine. Thermodynamic theory of structure, stability and fluctuations. J. Willey & Sons, 1971.

Grandy Jr, Walter T. Entropy and the time evolution of macroscopic systems. Vol. 10. Oxford University Press on Demand, 2008.

Grinstein, G., and R. Linsker. "Comments on a derivation and application of the ‘maximum entropy production’principle." Journal of Physics A: Mathematical and Theoretical 40, no. 31 (2007): 9717.

Hall, Charles AS. "The continuing importance of maximum power." Ecological modelling 178, no. 1-2 (2004): 107-113.

Hoang, Viet‐Ngu, and Mohammad Alauddin. "Analysis of agricultural sustainability: A review of exergy methodologies and their application in OECD countries." International Journal of Energy Research 35, no. 6 (2011): 459-476.

Hopkins, Milton N., and Eugene P. Odum. "Some aspects of the population ecology of breeding mourning doves in Georgia." The Journal of Wildlife Management 17, no. 2 (1953): 132-143.

Hovelius, Karolina. "Energy-, exergy-and emergy analysis of biomass production." (1997).

Hurley, Samantha, Anthony Tantuccio, Manuel Sebastian Escotet-Espinoza, Matthew Flamm, and Matthew Metzger. "Development and Use of a Residence Time Distribution (RTD) Model Control Strategy for a Continuous Manufacturing Drug Product Pharmaceutical Process." Pharmaceutics 14, no. 2 (2022): 355.

Jekayinfa, Simeon O., Kehinde M. Adeleke, Clement A. Ogunlade, B. F. Sasanya, and Nurudeen A. Azeez. "Energy and exergy analysis of Soybean production and processing system." Cleaner Engineering and Technology 10 (2022): 100540.

Jørgensen, Christian, Katja Enberg, Erin S. Dunlop, Robert Arlinghaus, David S. Boukal, Keith Brander, Bruno Ernande et al. "Ecology: managing evolving fish stocks." Science 318, no. 5854 (2007): 1247-1248.

Jørgensen, S. E. "Review and comparison of goal functions in system ecology." Vie et milieu (1980) 44, no. 1 (1994): 11-20.

Jørgensen, S. E., and H. Mejer. "A holistic approach to ecological modelling." Ecological Modelling 7, no. 3 (1979): 169-189.

Jørgensen, S. E., and Y. M. Svirezhev. "Teleology and extreme principles: A tentative Fourth Law of Thermodynamics." Towards a Thermodynamic Theory for Ecological Systems. Oxford, UK: Elsevier Ltd (2004): 301-322.

Jørgensen, Sven E., and Brian D. Fath. "Application of thermodynamic principles in ecology." Ecological complexity 1, no. 4 (2004): 267-280.

Jørgensen, Sven E., and Søren N. Nielsen. "Thermodynamic orientors: exergy as a goal function in ecological modeling and as an ecological indicator for the description of ecosystem development." In Eco targets, goal functions, and orientors, pp. 63-86. Springer, Berlin, Heidelberg, 1998.

Jørgensen, Sven Eric. "Integration of Ecosystem Theories: A pattern. Netherlands." (1992).

Jørgensen, Sven Erik, and Giuseppe Bendoricchio. Fundamentals of ecological modelling. Vol. 21. Elsevier, 2001.

Jorgensen, Sven Erik, and Yuri M. Svirezhev. Towards a thermodynamic theory for ecological systems. Elsevier, 2004.

Jørgensen, Sven Erik. "Parameters, ecological constraints and exergy." Ecological Modelling 62, no. 1-3 (1992): 163-170.

Kay, James J. "A nonequilibrium thermodynamic framework for discussing ecosystem integrity." Environmental Management 15, no. 4 (1991): 483-495.

Kay, James J., and Eric D. Schneider. "Thermodynamics and measures of ecological integrity." In Ecological indicators, pp. 159-182. Springer, Boston, MA, 1992.

Kay, Richard F. "1. On the Use of Anatomical Features To Infer Foraging Behavior in Extinct Primates." In Adaptations for foraging in nonhuman primates, pp. 21-53. Columbia University Press, 1984.

Kleidon, Axel. "Beyond Gaia: Thermodynamics of life and Earth system functioning." Climatic Change 66, no. 3 (2004): 271-319.

Kleidon, Axel. "Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (2010): 181-196.

Kozlowski, Jan. "Energetic definition of fitness? Yes, but not that one." The American Naturalist 147, no. 6 (1996): 1087-1091.

Loreau, Michel. "Ecosystem development explained by competition within and between material cycles." Proceedings of the Royal Society of London. Series B: Biological Sciences 265, no. 1390 (1998): 33-38.

Lotka, Alfred J. "Contribution to the energetics of evolution." Proceedings of the National Academy of Sciences 8, no. 6 (1922): 147-151.

Lotka, Alfred James. Elements of physical biology. Williams & Wilkins, 1925.

Ludovisi, Alessandro, Piera Pandolfi, and Maria Illuminata Taticchi. "The strategy of ecosystem development: specific dissipation as an indicator of ecosystem maturity." Journal of theoretical biology 235, no. 1 (2005): 33-43.

Månsson, B. Å., and J. M. McGlade. "Ecology, thermodynamics and HT Odum's conjectures." Oecologia 93, no. 4 (1993): 582-596.

Margalef, Ramon. "On certain unifying principles in ecology." The American Naturalist 97, no. 897 (1963): 357-374.

Margalef, Ramon. "Perspectives in ecological theory." (1968).

Marques, J. C., M. A. Pardal, S. N. Nielsen, and S. E. Jørgensen. "Analysis of the properties of exergy and biodiversity along an estuarine gradient of eutrophication." Ecological Modelling 102, no. 1 (1997): 155-167.

Marques, Renato, and Jacques Ranger. "Nutrient dynamics in a chronosequence of Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) stands on the Beaujolais Mounts (France). 1: Qualitative approach." Forest Ecology and Management 91, no. 2-3 (1997): 255-277.

Martyushev, Leonid M. "The maximum entropy production principle: two basic questions." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1545 (2010): 1333-1334.

Martyushev, Leonid M., and Vladimir D. Seleznev. "Maximum entropy production principle in physics, chemistry and biology." Physics reports 426, no. 1 (2006): 1-45.

Mauersberger, P. E. T. E. R. "Entropy control of complex ecological processes." Complex Ecology: The Part-Whole Relation in Ecosystems Englewood Cliffs, NJ, Prentice-Hall (1995): 130-165.

Mauersberger, Peter, and Milan Straškraba. "Two approaches to generalized ecosystem modelling: thermodynamic and cybernetic." Ecological Modelling 39, no. 1-2 (1987): 161-169.

Mauersberger, Peter. "On the role of entropy in water quality modelling." Ecological Modelling 7, no. 3 (1979): 191-199.

Mejer, Henning, and Sven Erik Jørgensen. "Exergy and ecological buffer capacity." In State-of-the-art in Ecological Modelling, pp. 829-846. Pergamon, 1979.

Mondal, Ayan, Nilanjan Das, and Sudipto Mandal. "Domesticatedation of rice reshaped associated biodiversity of rice field ecosystem." Journal of Animal Diversity 4 (2022): 0-0.

Morowitz, H.J. "Foundations of Bioenergetics. " Academic Press, New York, (1978) 344.

Morowitz, Harold J. "Energy flow in biology; biological organization as a problem in thermal physics." (1968).

Nielsen, S. N., and S. E. Jørgensen. "Goal functions, orientors and indicators (GoFOrIt's) in ecology. Application and functional aspects–Strengths and weaknesses." Ecological Indicators 28 (2013): 31-47.

Nielsen, Søren Nors, and Robert E. Ulanowicz. "Ontic openness: an absolute necessity for all developmental processes." Ecological Modelling 222, no. 16 (2011): 2908-2912.

Nielsen, Søren Nors. "Strategies for structural-dynamic modelling." Ecological Modelling 63, no. 1-4 (1992): 91-101.

Odum, Eugene P. "The Emergence of Ecology as a New Integrative Discipline: Ecology must combine holism with reductionism if applications are to benefit society." Science 195, no. 4284 (1977): 1289-1293.

Odum, Eugene P. "The Strategy of Ecosystem Development: An understanding of ecological succession provides a basis for resolving man's conflict with nature." science 164, no. 3877 (1969): 262-270.

Odum, Eugene P., and Alfred E. Smalley. "Comparison of population energy flow of a herbivorous and a deposit-feeding invertebrate in a salt marsh ecosystem." Proceedings of the National Academy of Sciences 45, no. 4 (1959): 617-622.

Odum, Eugene Pleasants, and Gary W. Barrett. Fundamentals of ecology. Vol. 3. Philadelphia: Saunders, 1971.

Odum, Howard T. "Environmental accounting: emergy and environmental decision making." (1996).

Odum, Howard T. "Explanations of ecological relationships with energy systems concepts." Ecological Modelling 158, no. 3 (2002): 201-211.

Odum, Howard T. "Self-organization, transformity, and information." Science 242, no. 4882 (1988): 1132-1139.

Odum, Howard T. "Systems Ecology; an introduction." (1983).

Odum, Howard T., and Richard C. Pinkerton. "Time's speed regulator: the optimum efficiency for maximum power output in physical and biological systems." American Scientist 43, no. 2 (1955): 331-343.

Onsager, Lars. "Reciprocal relations in irreversible processes. I." Physical review 37, no. 4 (1931): 405.

Paltridge, Garth W. "Global dynamics and climate‐a system of minimum entropy exchange." Quarterly Journal of the Royal Meteorological Society 101, no. 429 (1975): 475-484.

Patten, Bernard C. "Network integration of ecological extremal principles: exergy, emergy, power, ascendency, and indirect effects." Ecological modelling 79, no. 1-3 (1995): 75-84.

Patten, Bernhard C. "On the quantitative dominance of indirect effects in ecosystems." In Developments in Environmental Modelling, vol. 5, pp. 27-37. Elsevier, 1983.

Prigogine, I. "Etude Thermodynamique des Phenomenes Irreversibles, Desoer, Liege." (1947).

Prigogine, I. "Introduction to Thermodynamics of Irreversible Processes. American Lecture Series, Vol. 185. Charles C." (1955).

Prigogine, I. "Thermodynamics of Irreversible Processes." Wiley, (1995), New York.

Prigogine, I. "Time, Structure, and Fluctuations". Science 201 (1978): 777-785.

Radtke, E., and M. Straškraba. "Self-optimization in a phytoplankton model." Ecological Modelling 9 (1980): 247-268.

Ray, Santanu. "Extremal principles with special emphasis on exergy and ascendency—the modern approach in theoretical ecology." Journal of Biological Systems 14, no. 02 (2006): 255-273.

Schneider, Eric D., and James J. Kay. "Life as a manifestation of the second law of thermodynamics." Mathematical and computer modelling 19, no. 6-8 (1994): 25-48.

Schneider, Rebecca L., and Rebecca R. Sharitz. "Hydrochory and regeneration in a bald cypress‐water tupelo swamp forest." Ecology 69, no. 4 (1988): 1055-1063.

Schramski, John R., Anthony I. Dell, John M. Grady, Richard M. Sibly, and James H. Brown. "Metabolic theory predicts whole-ecosystem properties." Proceedings of the National Academy of Sciences 112, no. 8 (2015): 2617-2622.

Schrodinger, E., and IS LIFE WHAT. "The physical aspect of the living cell." What is Life (1944): 70-71.

Sheng, Xiabing, Zhizhong Sun, Xuefeng Wang, Yanning Tan, Dong Yu, Guilong Yuan, Dingyang Yuan, and Meijuan Duan. "Improvement of the rice “easy-to-shatter” trait via CRISPR/Cas9-mediated mutagenesis of the qSH1 gene." Frontiers in plant science 11 (2020): 619.

Straškraba, Milan. "Natural control mechanisms in models of aquatic ecosystems." Ecological Modelling 6, no. 4 (1979): 305-321.

Tilley, David Rogers. "Howard T. Odum’s contribution to the laws of energy." Ecological Modelling 178, no. 1-2 (2004): 121-125.

Ulanowicz, Robert E. "An hypothesis on the development of natural communities." Journal of theoretical Biology 85, no. 2 (1980): 223-245.

Ulanowicz, Robert E. "Ecosystem integrity: a causal necessity." In Perspectives on Ecological Integrity, pp. 77-87. Springer, Dordrecht, 1995.

Ulanowicz, Robert E. "Life after Newton: an ecological metaphysic." BioSystems 50, no. 2 (1999): 127-142.

Ulanowicz, Robert E. "Some steps toward a central theory of ecosystem dynamics." Computational Biology and Chemistry 27, no. 6 (2003): 523-530.

Ulanowicz, Robert E. Growth and development: ecosystems phenomenology. Springer Science & Business Media, 2012.

Ulanowicz, Robert E., and James J. Kay. "A package for the analysis of ecosystem flow networks." Environmental Software 6, no. 3 (1991): 131-142.

Volvenko, I. V. "Extremal principles and goal functions of biocenotic systems." Biophysics 57, no. 3 (2012): 350-362.

Yen, Jian DL, David M. Paganin, James R. Thomson, and Ralph Mac Nally. "Thermodynamic extremization principles and their relevance to ecology." Austral Ecology 39, no. 6 (2014): 619-632.

Yıldızhan, Hasan. "Energy and exergy utilization of some agricultural crops in Turkey." Thermal Science 23, no. 2 Part A (2019): 813-822.

Zhou, Jizhong, Shijun Ma, and George W. Hinman. "Ecological exergy analysis: a new method for ecological energetics research." Ecological modelling 84, no. 1-3 (1996): 291-303.

Additional Files



How to Cite

Mondal, A., Das, N., Banerjee, R., Batabyal, S., Gangopadhyay, S., Ray, H., Biswas, N., & Mandal, S. (2023). Investigating the Health of a Rice Field Ecosystem Using Thermodynamic Extremal Principles. Ecology, Economy and Society–the INSEE Journal, 6(1), 81–108.



Special Section: Rehabilitating Degraded Ecosystems