







































Ecology, Economy and Society–the INSEE Journal 6(1): 81-108, January 2023 

RESEARCH PAPER 

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

Ayan Mondal, Nilanjan Das,** Rituparna Banerjee,*** Sunanda 
Batabyal,**** Sohini Gangopadhyay,***** Harisankar Ray,# Nivedita 

Biswasd,   Sudipto Mandal### 

Abstract: 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 

 
 Ecology and Environmental Modelling Laboratory, Department of Environmental Science, 
University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 

mondalayan.zoo@gmail.com 

** Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, 
Indianilanjandas1995@gmail.com 

*** Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 
rituparna93banerjee@gmail.com 

**** Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 
sunanda.envs@gmail.com 

***** Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 
aslgsohini@gmail.com 

# Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 
rayharisankar1996@gmail.com 

  Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 

niveditabiswas.1143@gmail.com 

### Ecology and Environmental Modelling Laboratory, Department of Environmental 
Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. 
sudipto11@gmail.com 

Copyright © Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 2023. 
Released under Creative Commons Attribution © NonCommercial 4.0 International licence 

(CC BY-NC 4.0) by the author.  

Published by Indian Society for Ecological Economics (INSEE), c/o Institute of  Economic 
Growth, University Enclave, North Campus, Delhi 110007.  

ISSN: 2581–6152 (print); 2581–6101 (web).  

DOI: https://doi.org/10.37773/ees.v6i1.925  

mailto:mondalayan.zoo@gmail.com
mailto:nilanjandas1995@gmail.com
mailto:rituparna93banerjee@gmail.com
mailto:sunanda.envs@gmail.com
mailto:aslgsohini@gmail.com
mailto:rayharisankar1996@gmail.com
mailto:niveditabiswas.1143@gmail.com
mailto:sudipto11@gmail.com
https://doi.org/10.37773/ees.v6i1.925


 Ecology, Economy and Society–the INSEE Journal [82] 

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. 

Keywords: Far-from-equilibrium system; goal-function; rice field ecosystem; 
thermodynamic ecology 

 

1. INTRODUCTION 

Ecosystems are complex, hierarchic, adaptive, and organized, as they are 
comprised of many components. These biotic and abiotic components 
interact to produce new emergent states that are impossible to predict 
accurately (Nielsen and Ulanowicz 2011). However, ecosystems exhibit 
certain common structural and functional characteristics that suggest they 
are driven by some directive principles that determine their future 
trajectories, such as the extremal principle of least action. Modern research 
in ecology aims to test the application of various goal functions in 
characterizing ecosystems’ structure and evolution (Mauersberger and 
Straškraba 1987; Jørgensen et al. 2007). Using goal functions in ecology 
simplifies ecological modelling and stability concepts by introducing 
extremal principles from which the “integral features” of the ecosystem can 
be derived (Mauersberger and Straškraba 1987; Jørgensen et al. 2007). 
According to Nielsen and Jørgensen (2013), there are three goal functions: 
biotic, network, and thermodynamic. Biotic goal functions are related to 
biodiversity, biomass, species number, richness, and evenness while 
network goal functions involve flow matrix, respiration, and import–export 
analysis (Ulanowicz 1986; Baird and Ulanowicz 1989; Christensen and 
Pauly 1992; Fath and Patten 1999). Thermodynamic goal functions, 
summarized by Yen et al. (2014), essentially seek to maximize or minimize a 
thermodynamic property of the macroscopic state of the system. These 
include a large set: “maximum exergy storage” (Jørgensen and Svirezhev 
2004), “maximum energy storage” (Odum 1988), “maximum residence 



[83] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

time” (Fath, Patten, and Choi 2001), “maximum entropy production” 
(Dewar 2010; Kleidon 2010), “minimum entropy production” (Prigogine 
1995; Martyushev and Seleznev 2006), “min-max principle of entropy 
production” (Aoki 2006), “maximum rate of gradient degradation” 
(Schneider and Kay 1994), “maximum power” (Lotka 1922; Brown, 
Marquet, and Taper 1993; DeLong 2008), “maximum empower” (Odum 
and Pinkerton 1955), “maximum ascendency” (Ulanowicz 1980, 2003), 
“minimum specific energy dissipation” (Margalef 1963), “constructal law of 
evolution” (Bejan and Lorente 2010), and “maximum rate of cycling” 
(Morowitz 1968). Several of these different quantities are, in fact, equivalent 
or complementary, as explained by several researchers (Jørgensen 1992, 
1994; Patten 1995; Jørgensen and Nielsen 1998; Fath, Patten, and Choi 
2001; Ray 2006; Yen et al. 2014). 

Limits and extremal principles are found to order many natural phenomena, 
such as animal sizes and the heights of mountain chains, and provide a 
rationale to order masses of data in an analytical framework. Indeed, the 
first such principle to explain ecological processes was formulated in 1859 
by Darwin as the “survival of the fittest”—those ablest to harvest the 
available resources. The recognition of ecological systems as open systems 
powered by the sun and maintaining a dynamically stable state by 
exchanging energy and materials from their surroundings—like a 
thermodynamic engine—led Lotka to propose in the 1920s that ecosystems 
flourished by maximizing the rate of entropy production. Several related 
extremal principles have been formulated (Figure 1) towards developing the 
ecology theory since then. However, the examples of testing these in the 
field are still too few to warrant a clear direction. 

In this study, we present an application of four of these formulations to 
data from rice fields to test their relative or collective fruitfulness in 
explaining the growth trajectory of rice plants. These are based on the 
concepts of energy, exergy, total systems throughflow, and ascendency. 

2. DATA AND APPLICATION OF THE EXTREMAL 
PRINCIPLE 

The experiment was carried out at two sites: The Crop Research and Seed 
Multiplication Farm (CRSMF) (Lat: 23°15'4.09"N, Lon: 87°50'41.05"E) for 
the ecosystem of domesticated rice fields and Bamchandaipur village (Lat: 
23°13'35.95"N, Lon: 87°54'34.34"E) for the ecosystem of wild rice fields in 
Purba Bardhaman district, West Bengal, India (Figure 2). 

 



 Ecology, Economy and Society–the INSEE Journal [84] 

Figure 1: A Chronological Snapshot of Different Propositions and Events 
Depicting the Evolution in the Concept of Goal Functions Through Time 

 

Source: Authors 

Figure 2: Study Sites of Domesticated (Left) and Wild Rice Field (Right) 

Ecosystems 

 

Source: Authors 

2.1. Data Collection 

Field sampling was carried out for three consecutive years, from March 
2016 to June 2019. The sampling was carried out at weekly intervals during 
the morning (7:00–10:00 IST) and evening (15:00–18:00 IST) hours 
throughout the study period. Accordingly, there were 170 sampling days 
during the entire study. There are four zones in the rice field ecosystem: 
benthic or littoral, limnetic, transitional, and terrestrial. Various forms of 



[85] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

sampling were used for the multiple taxa occupying each zone to record 
total biodiversity. Water and soil collection and sweeping were done 
through a randomized complete block design method to reduce sampling 
bias. The eight functional compartmental guilds were assigned based on 
trophic levels—green plants as producers, phytophagous as herbivores, 
predators as carnivores, omnivores, detritivores, and parasitoids. In some 
cases, where direct observation of food habits was not possible, a coffee-
table experiment was performed to determine the food preferences, and the 
guild was assigned accordingly. All the collected and calculated data are 
provided in Appendix 1. Water-level data for wild rice fields were recorded 
at weekly intervals throughout the year and averaged to identify the 
monthly values (Figure 5). 

2.2 The Extremal Principles Tested in this Study 

Four thermodynamic extremal principles were tested on the rice field data 
described in the previous section. These are emergy, exergy, total system 
throughflow, and ascendency; and are outlined here: 

2.2.1. Energy 

Energy and exergy, the two target functions, are based on thermodynamics. 
Emergy, or embodied energy (Odum 1983), is a concept that assesses how 
much solar radiation is required to create a particular organism (biomass). 
The biomass, or its free energy, is multiplied by a factor determined by the 
amount of solar energy required to generate one unit of energy in the 
organism. The number of transfer and transformation stages a system has 
taken away from its input source is assumed to increase the quality of 
energy brought into it and its energy content. Because they are farther away 
from solar-energy inputs than photosynthesizing primary producers, upper 
trophic-level animals in ecosystems are thought to have a higher energy 
quality. 

2.2.2. Exergy 

The amount of work a system can do when it is brought into equilibrium 
with its surroundings is thermodynamically characterized as exergy. Exergy 
attempts to account for both the free energy stored in biomass and the free 
energy stored in information. Exergy represents the quality of the 
ecosystem’s energy. The expression for exergy calculation proposed by 
Mejer and Jørgensen (1979) is 

                          (1) 



 Ecology, Economy and Society–the INSEE Journal [86] 

Where R = gas constant, T = absolute temperature, ci = concentration in 
the ecosystem of the component, i. Index 0 = inorganic components of the 
considered chemical element and ci

eq = corresponding concentration of ith 
component at the thermodynamic equilibrium. 

Boltzmann’s constant (1.3803 × 10-23 J molecules-1 deg-1) equals kT lnI, 
where I is the pieces of information we have about the state of the system 
and k is Boltzmann’s constant (1.3803 × 10-23 J molecules-1 deg-1). This 
means that the exergy of one bit of information is equal to kT ln2. 
Information transfer from one system to another is frequently a nearly 
entropy-free energy transfer. 

As an ecosystem grows, it becomes increasingly successful in capturing and 
dissipating the exergy of incoming solar radiation (Schneider and Kay 
1994). Schneider and Kay (1994) propose the dissipation of exergy as a 
target function. This exergy is employed to create and maintain organization 
and structure. Exergy accounts for the biomass and information stored in it; 
therefore, increased nutrient concentrations will likely result in more exergy. 
The ability to account for the system’s ability to use available resources 
would be beneficial. The concept of specific exergy is used to describe this 
ability, which is defined as (Equation 2): 

                          (2) 

Where β = quality factor, calculated based on the amount of information 
embedded in the genes, and X = biomass concentration of the ith species 
relative to the total biomass concentration. 

When the temperatures of the two systems vary, the entropy lost by one 
system does not equal the entropy acquired by the other. Still, the exergy 
lost by one system equals the exergy transferred and obtained by the other. 
In this case, exergy is more convenient than entropy. Exergy can be used to 
express the second rule of thermodynamics as follows (Equation 3): 

            (3) 

This implies that exergy is always lost, that is, work is lost as heat that 
cannot be used to perform work. The entropy and exergy formulations of 
the second law of thermodynamics are, of course, interchangeable. 

2.2.3 Total System Throughflow (TST) 

The first quantitative attempt to quantify ecosystem growth was Lotka’s 
“maximum power idea” (Lotka 1932, which defined power as work per unit 
of time. The concept evolved into a theory by Odum and Pinkerton (1955), 



[87] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

who stated that ecosystems act to maximize their power output. TST refers 
to the energy flow throughout the entire system (Equations 4 and 5). 

            (4) 

             (5) 

Where j=1, 2,…,n  

Although this concept was not explicitly related to energy quality or system 
organizational traits, it was indicated that systems that generated more 
power were better suited and favoured in evolutionary selection. 

2.2.4 Ascendency 

Ulanowicz (1986) created the concept of ascendency to account for the 
throughflow of energy in an ecosystem (T) and network (A). Ascendency 
refers to the part of a system’s intercompartmental articulation that is 
dictated by the entire complexity of the collection of processes that 
corresponds to organized flows and is weighted by the TST (Equation 6). 

                          (6) 

Maximizing this aim function should describe the autocatalytic tendencies 
inherent in structuring emerging ecological networks. 

Ascendency takes into account the network’s size (T) and the information 
contained inside it. A is a massive variable; the size term T is the most 
important in most calculations (Equation 7). 

             (7) 

As a result, the structural exergy should be firmly linked to A-T, whereas 
the exergy should be more strongly linked to the size term T but perhaps 
also to A because T is the most dominating term. 

Average mutual information is dimensionless and has a limited range of 
values—generally between 2.0 and 6.0. In non-negative real values, TST—
which scales this information quantity—can be highly variable. As a result, 
the ascendency metric is dominated by throughflow, resulting in highly 
correlated findings for power and ascendency (Jorgenson 1992). 

2.3. Model Development 



 Ecology, Economy and Society–the INSEE Journal [88] 

An eight-compartment model was constructed (Table 1 and Figure 3) to 
evaluate the interrelationship among extremal principles and subsequent 
stability analysis. The components of the model are presented in Table 1. 

The model used these components as state variables to calculate the 
extremal principles. 

Table 1: The Eight Major Components (Producer, Herbivore, Carnivore, Detritus, 
Detritivore, Omnivore, and Parasitoid) with Examples  

Components Examples Components Examples 

Producer 

 

Detritivore 

 

Herbivore 

 

Omnivore 

 

Carnivore 

 

Parasitoid 

 

Detritus 

 

Nutrient 

 

Source: Authors 

The description of equations (Eq) and symbols are given in Appendices 1 
and 2. Equation 8 describes the carnivore dynamics, with inflows primarily 
based on pred, detcarn, and pred1 and outflows primarily based on mortfish, refi, 
omni3, and para3. Herbivores and carnivores both had an impact on 
predation (Eq 8.1). Carnivores and detritivores both had an impact on the 
detcarn (Eq 8.2). Carnivores and omnivores both had an impact on pred1 (Eq 
8.3). Only carnivores had an impact on both the mortfish (Eq 8.4) and refi 
(Eq 8.5). Carnivores and omnivores influenced the omni3 (Eq 8.6). 
Carnivores and para were both affected by para3 (Eq 8.7). 

Eq 9 describes the detritus dynamics, with inflows primarily based on 
mortfish, mz, mort, mortomni, and mortpara and outflows primarily based on 
outdet, detfed, and omni5. Carnivores had an impact on the mortfish (Eq 9.1). 
Carnivores and herbivores both had an impact on the mz (Eq 9.2). 
Herbivores and producers had a consequence on the mort (Eq 9.3). The 



[89] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

omnivores influenced the mortomni (Eq 9.4). Para had an impact on the 
mortpara (Eq 9.5). Detr and qv influenced the outlet (Eq 9.6). Detr and water 
level had an impact on the detfed (Eq 9.7). Omnivore and detr were both 
influences on the omni5 (Eq 9.8). 

Eq 10 can be used to define the detritivore dynamics. Detfed is the most 
common inflow, whereas detexcr, detcarn, omni4, para5, and rdetri are the most 
common outflows. Detr and water level had an impact on the detfed (Eq 
10.1). Detritivore and water level both influenced the detexcr (Eq 10.2). 
Carnivores and detritivores both had an impact on the detcarn (Eq 10.3). 
There were detritivore and omnivore influences on the omni4 (Eq 10.4). 
Detritivore and para5 both had an impact on para5 (Eq 10.5). Detritivores 
affected the rdetri (Eq 10.6) Eq 11 describes the herbivore dynamics, with 
inflows mostly based on gr and outflows depending on pred, mz, rz, omni2, 
and para5. Herbivores and producers had an impact on the gr (Eq 11.1). 
Herbivores and carnivores both had an impact on predation (Eq 11.2). 
Herbivores and carnivores had an impact on the mz (Eq 11.3). Herbivores 
had an impact on the rz (Eq 11.4). Herbivore and omnivore interactions 
altered the omni2 (Eq 11.5). Herbivore and para were both impacted by 
para5 (Eq 11.6). 

Eq 12 can be used to define nutrient dynamics. Outflows are primarily 
based on up and outn while inflows are primarily based on input and detexcr. 
Nutin, qv, and the water level all had an impact on the input (Eq 12.1). 
Detritivores and the water level both influenced the detexcr (Eq 12.2). Nutr, 
producers, and the water level all had an impact on the upt (Eq 12.3). Nutr 
and qv had an impact on the outn (Eq 12.4). 

Eq 13 can be used to define the omnivore dynamics; outflows are primarily 
based on mortomni, pred1, para4, and romni. In contrast, inflows are primarily 
based on omni1, omni2, omni3, omni4, and omni5. Producers and omnivores 
had an impact on the omni1 (Eq 13.1). Herbivore and omnivore interactions 
altered the omni2 (Eq 13.2). Carnivores and omnivores influenced the omni3 
(Eq 13.3). There were detritivore and omnivore influences on the omni4 (Eq 
13.4). Detr and omnivore had an impact on the omni5 (Eq 13.5). The 
omnivore had an impact on the mortomni (Eq 13.6). Carnivores and 
omnivores both had an impact on pred1 (Eq 13.7). Para and omnivores had 
an influence on para4 (Eq 13.8). The omnivorous had an impact on the 
romni (Eq 13.9). 

Eq 14 can be used to define parasite dynamics. Outflows depend primarily 
on mortpara and rpara while inflows are primarily based on para1, para2, 
para3, para4, and para5. Para and producer had an impact on para1 (Eq 14.1). 



 Ecology, Economy and Society–the INSEE Journal [90] 

Para and herbivore had an effect on para2 (Eq 14.2). Para and carnivore had 
an impact on para3 (Eq 14.3). Para and omnivore had an impact on para4 
(Eq 14.4). Para and detritivore affected para5 (Eq 14.5). Para impacted the 
mortpara and rpara (Eq 14.6, 14.7). 

Figure 3: The Calculation Framework of Extremal Principles Values in STELLA 
9.0  

 

Source: Authors 

Eq 15 can be used to define the producer dynamics. Upt and uptc are the 
most common inflows whereas gr, mort, out ph, omni1, para1, and rpro are the 
most common outflows. Nutr, producers, and the water level all had an 
impact on the upt (Eq 15.1). Up had an impact on the uptc (Eq 15.2). 
Producers and herbivores both had an impact on the gr (Eq 15.3). 
Producers and herbivores both had an impact on the mort (Eq 15.4). qv and 
producers influenced the out ph (Eq 15.5). Omnivores and producers had an 
impact on the omni1 (Eq 15.6). Para and producers had an impact on para1 
(Eq 15.7). Producers had an impact on the rpro (Eq 15.8). 



[91] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

The sums of rdetri, refi, romni, rpara, rpro, and rz was utilized to determine 
dissipation in Eq 16. The exergy dynamics can be defined using Eq 17, 
which is the sum of all the producers, herbivores, omnivores, carnivores, 

deter and detritivores, and para. Where the values of  and 

. When the TST was divided by TSS, Eq 18 was used to 

calculate the residence time. When the dissipation was divided by 
throughflow-derived storage (TSS), Eq 19 was utilized to define the specific 
dissipation. When the exergy was divided by TSS, Eq 20 was utilized to 
define the specific exergy. Eq 21 can be used to calculate the TSS, which is 
the sum of all of the carnivore, detritivore, herbivore, omnivore, para, and 
producer populations. The TST is defined by Eq 22 as the sum of detcarn, 
detexcr, detfed, gr, mort, mortfish, mortomni, mortpara, mz, omni1, omni2, omni3, 
omni4, omni5, para1, para2, para3, para4, para5, pred, pred1, and upt (Refer 
Appendix 1). 

3. RESULT AND DISCUSSION 

3.1. Integration of Goal Function 

Theoretical approaches have dominated the investigation of the 
thermodynamic extremization principle. Consistencies between energy 
storage and dissipation showed that existing thermodynamic extremization 
principles might be unified. Hence, interaction between the two categories 
(energy storage and dissipation) is possible. 

Based on the aforementioned theories, the extremal principles could be 
integrated as shown in Figure 5. Maximal energy storage implies maximum 
energy dissipation (metabolic rate). Because living species always dissipate 
energy, an ecological system can improve energy dissipation by increasing 
energy storage (biomass) until the energy storage reaches a maximum (that 
is, the system becomes resource-limited). By combining maximum energy 
dissipation and maximum energy storage, all thermodynamic extremization 
concepts are compatible. 

Numerous thermodynamic extremization principles have been proposed 
and applied to ecological issues. Many of the energy quantities have been 
linked (Figure 4) to ecological quantities including biomass, food-web 
complexity (e.g., link density), growth rates, life-cycle duration, and 
community stability, all of which have been shown to follow predictable 
trajectories during ecosystem evolution (Odum 1969; Loreau 1998). The 
relevant literature is scattered and distinguishing between possible 
extremization principles has received much attention. Despite their 
apparent differences, multiple thermodynamic extremization principles may 



 Ecology, Economy and Society–the INSEE Journal [92] 

be boiled down to two main themes: energy storage and dissipation (Fath, 
Patten, and Choi 2001). Various energy storage and energy dissipation 
principles are discussed in their paper. 

Figure 4: Mathematical Integration of Extremal Principles 

 

Source: Authors 
Note: All acronyms have been elaborated in paragraph 2.2  

According to energy-dissipation principles, natural systems utilize energy at 
extreme rates. Maximum energy dissipation indicates high throughput 
whereas minimum energy dissipation indicates efficient energy utilization 
(that is, organisms using energy as fast as possible). Maximum energy 
dissipation does not always imply poor use of other resources—such as 
water or nutrients—as efficient use of these resources is sometimes 
required for high energy dissipation. In this study, two scenarios are 
considered: maximum entropy creation and maximum power. According to 
the principle of maximal entropy production (MEP), all non-equilibrium 
thermodynamic systems produce entropy as quickly as feasible, returning 
the system to a state of maximum entropy as soon as possible (Martyushev 
and Seleznev 2006). Several attempts have been made to derive generic 
proof for far-from-equilibrium systems (Dewar 2003, 2005), but none have 
been successful (Grinstein and Linsker 2007). The rate of “useful” energy 
usage (e.g., conversion to biomass or reproduction) (Jorgensen and 
Svirezhev 2004), the rate of “emergy” use (Odum 1996, Hall 2004, Tilley 
2004), and “fitness” or rate of reproduction have all been linked to power 
(Brown, Marquet, and Taper 1993). Loreau (1998) proposes that adequate 
definitions of power should be based on ecological processes because each 
of these definitions of power only covers one component of energy 
consumption (e.g., demography, resource use). 

The exergy principle has been provided as a tentative thermodynamic law 
that might be used as a hypothesis in the present research. Ecosystems have 



[93] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

a lot of different paths and much exergy flowing through them. Increases in 
system features such as distance from thermodynamic ground, structure, 
heterogeneity, organization, gradients, and energy quality result from 
incremental exergy increases that accompany rising path lengths. As 
throughflows increase with the increase of path length, this feature becomes 
more aligned with exergy and emergy. ASC (ascendency) in ecosystem 
networks leads to the maximum of these values because TST corresponds 
to power output, which is often a substantial component of ascendency. As 
a result, the four extreme principles of exergy maximization, emergy, power, 
and ascendency are linked by a single process: exergy propagation in 
ecological networks. According to our findings, exergy, emergy, power, and 
ascendency are all found in the structure and microscopic dynamics of 
energy, matter flows, and storages in ecosystems. 

3.2. Health of Rice Field Ecosystem in Relation to the Extremal 
Principles 

The present study showed that nutrition and water level are the most 
important and main regulatory parameters for wild and domesticated rice 
field ecosystems. 

The nutrient content and water level in domesticated and wild rice fields 
were different. The nutrient content of a domesticated rice field was 40 
mgCg-1 but only 18 mgCg-1 in a wild rice field environment. Water 
concentration in domesticated rice field systems varies between 2.8–12 cm, 
but in wild rice field systems, it varies between 10–70 cm due to higher 
rainfall during monsoon seasons. Figure 5 depicts the water level in the 
domesticated and wild rice field ecosystems. Figures 6 and 7 describe the 
conditions of extremal principles in the domesticated and wild rice field 
ecosystems, respectively. 

Zehe et al. (2010) studied the maximum energy dissipation and the 
connection between water flow and soil structure. They concluded that 
biological soil structures are crucial for infiltration and soil water flow. 
Hence, the burrows created by the worms allow for a more efficient 
redistribution of water within the soil, which implies a more efficient 
dissipation of free energy. In the present comparison, the maximum 
dissipation values for the domesticated rice field ecosystem touch 175 KJ 
near around 100 days of rice cultivation and then decrease with time, 
whereas, in the wild rice ecosystem, the value is nearly 16 KJ around 120 
days of cultivation and remain stable throughout the study period. Hence, it 
could be said that the water flow of the domesticated rice fields was 
controlled and infiltration of the water-forming network within the soil 



 Ecology, Economy and Society–the INSEE Journal [94] 

structure is temporary with high dissipative energy—implying higher 
entropy production. However, no such mechanism occurred in the wild rice 
ecosystem. The field was a natural wetland system and was always 
inundated by water flow depending upon rainfall. Although the values of 
maximum dissipation were lower than domesticated fields, the value (17.5 
KJ) reached an asymptote beyond the shattering of rice seeds, implying 
lower entropy in the system. Sheng et al. (2020) add that the shattering of 
rice seeds is an evolutionarily beneficial phenomenon for wild rice varieties. 
This trait is beneficial for dispersal, preventing the seeds from drying and 
losing seed dormancy. 

Figure 5: Temporal Variation of Water Levels in Domesticated (Annual Plant) and 
Wild Rice (Perennial Plant) Field Ecosystems 

 

Source: Authors 

In the present study, the minimum specific dissipation of the domesticated 
rice field ecosystem was constant (0.020) during rice cultivation. However, 
the values are a bit higher for wild rice fields (0.020–0.040), meaning the 
values were greater till the panicle initiation stage of rice and behaved the 
same as domesticated fields after the development of reproductive 
structures. Ludovisi, Pandolfi, and Taticchi (2005) propound that specific 
dissipation is a good indicator of ecosystem health. Moreover, the higher 
the specific dissipation of a system, the lower the capacity of a system to 
convert the incoming entropy energy into internal organization. The 
nutrient input of the wild rice fields was non-controlled, resulting in 
differential resource utilization by the rice plants until the crop reached its 
sexual maturity. After the panicle initiation period to shattering, the system 
behaved quite self-organized. However, in the domesticated fields, the 
nutrient input was controlled throughout the study. Hence, all the rice 
plants showed high productivity and greater self-organization compared 



[95] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

with wild rice throughout the period, from germination to harvest. Despite 
having higher entropy in the system, the rice plants managed the nutrients 
efficiently in the domesticated rice fields. 

Hovelius (1997) compared the exergy and energy values for salix, winter 
wheat, and winter rape cultivation in Sweden. She reports that the exergy 
values were always greater than the energy values depicting the quality of 
energy utilized by the crops. In the domesticated rice fields, the values 
ranged between 350,000–400,000 KJ, which was 10 times higher than the 
wild rice fields throughout the study, confirming the better energy quality in 
the system. It also showed better resource utilization and nutrient 
accumulation in the biomass of rice seeds in the domesticated rice fields. 
The values in the wild rice fields increased like a growth curve and reached 
an asymptote after shattering, implying the gradual accumulation of 
nutrients throughout the growth period. However, the values increased till 
crop maturity in the domesticated rice field and then decreased after 
harvest, that is, the post-harvest situation of rice straws in the field. The 
present findings are in agreement with Hoang and Alauddin (2011). 
Jekayinfa et al. (2022) observed that the use of machinery in the processing 
and production of soybean crops fetches higher exergy values. In the 
domesticated rice fields, the labour cost, tractors for irrigation, use of 
fertilizers and pesticides, and weeding resulted in higher cumulative exergy 
values than in the wild rice fields. Similar results were obtained by Yıldızhan 
(2017) during his study on wheat production in Turkey. 

The minimum specific exergy was almost identical for wild and 
domesticated rice field ecosystems (40 KJ kg-1 oC), showing no change in 
the specific exergy at each phenological stage from germination to 
shattering in the wild rice fields. However, variation was observed for 
domesticated rice fields. Hence, minimal useful work was observed for 
domesticated rice fields. The wild rice field ecosystem possesses more 
faunal biodiversity than the domesticated rice fields, resulting in a complex 
food web and more ecological interactions among the organisms. Hence, 
the specific exergy change between the two trophic levels is minimum and 
uniform. However, the man-made or domesticated system is destroyed after 
a certain time or harvest. Also, irrigation destroys the soil structure, altering 
the existing biodiversity and specific exergy. 

The average maximum residence time in the domesticated rice fields was 
(0.6), while in the wild rice fields, it was (0.35)—showing higher 
throughput-derived storage in the previous field than the latter with the 
same TST values. Schramski et al. (2015) advocate that the average 



 Ecology, Economy and Society–the INSEE Journal [96] 

residence time of an ecological system is dependent upon the body size, 
temperature, and structural organization of the system. With the increase of 
species number in the wild rice fields, the TST, maximum power, or cycling 
of the nutrients and energy transfer was low compared to domesticated rice 
fields. The maximum storage (TSS) was almost 10 times higher in the 
domesticated fields. Hence, the ratio between TSS and TST appeared to be 
small for the wild rice system. 

Figure 6: Temporal Variation of Seven Different Extremal Principles (Dissipation, 
Exergy, Residence Time, Specific Dissipation, Specific Exergy, TSS-storage, TST-
power) in the Domesticated Rice Field Ecosystem 

 

Source: Authors 

 

 

 

 

 

 

 

 



[97] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

Figure 7: Temporal Variation of Seven Different Extremal Principles (Dissipation, 
Exergy, Residence Time, Specific Dissipation, Specific Exergy, TSS-storage, TST-
power) in the Wild Rice Field Ecosystem 

 

Source: Authors 

4. CONCLUSIONS 

The present research shows that current extremization theories could be 
merged to exhibit a pattern of significant correlation. This integration of 
extremization ideas ought to make using them easier and enable a change in 
emphasis toward empirical investigations. 

It could be concluded that maximum dissipation and maximum exergy 
progressed apace with that of maximum storage till the maturation of rice 
and became stable thereafter. In contrast, maximum residence time and 
maximum specific dissipation values initially decreased before their 
asymptotic rise. A similar pattern was also observed for maximum specific 
exergy. However, the maximum power dissipation curve followed a highly 
fluctuated course before becoming stable on the maturation of rice. 

Although they are uncommon, empirical investigations of thermodynamic 
extremization principles are crucial to our comprehension and use of these 
strategies. We used a dynamic ecosystem modelling technique in wild and 
domesticated rice fields to see how they reacted to various environmental 
conditions. This result indicates that wild rice fields are healthier and more 
stable than domesticated ones. Our approach might be modified to forecast 
a wider variety of ecological patterns that could help determine how 
applicable thermodynamic concepts are to ecology. Exciting areas of study 



 Ecology, Economy and Society–the INSEE Journal [98] 

include the development of quantitative theories and the empirical 
verification of these hypotheses, which should make it easier to apply 
thermodynamic concepts to common ecological issues. 

ACKNOWLEDGEMENTS 

The authors would like to thank the funding agency, SERB, DST, 
Government of India, New Delhi, (Project No. EMR/2016/002618) for 
conducting the research work. The authors also acknowledge the 
agricultural scientists of the Department of Agriculture, Government of 
West Bengal, and the officials of the Crop Research and Seed Multiplication 
Farm, The University of Burdwan, for extending their help and valuable 
suggestions for the research. The authors declare no conflict of interest. 

 

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[103] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

APPENDIX 1: Symbols and Initial Inputs Used in the Construction of the Model 1 

Symbol Explanation Values and Equations 

pred Predation rate of carnivore upon 
herbivore 

IF (herbivore>3) THEN (0.1*carnivore*(herbivore-0.1)/(1+herbivore)) ELSE (0) 

detcarn Predation rate of carnivore upon 
detritivore 

0.33*carnivore*0.17*detritivore/(detritivore+1) 

pred1 Predation rate of carnivore upon 
omnivore 

0.1*carnivore*(omnivore-0.1)/(0.5+omnivore) 

mortfish Mortality rate of carnivore 0.02*carnivore 
refi Respiratory rate of carnivore 0.06*carnivore 
omni3 Predation rate of omnivore upon 

carnivore 
0.04*(carnivore-0.1)*(0.2*omnivore)/(carnivore+2) 

para3 Parasitization rate of 
parasite/parasitoid upon carnivore 

carnivore*para*0.00001 

mz Mortality rate of herbivore 0.2*herbivore+0.04*carnivore*(herbivore-0.1)/(1+herbivore) 
mort Mortality rate of producer 0.25*producer+0.17*(producer-0.1)*herbivore/(producer+2) 
mortomni Mortality rate of omnivore 0.034245*omnivore 
mortpara Mortality rate of parasite/parasitoid para*0.03 
outdet Outflow rate of detritus detr*(qv+0.9) 
detfed Feeding rate of detritivore upon 

detritus 
(0.1*detr)++((IF (waterlevel<10) THEN (waterlevel*detr/3) ELSE (detr/3))) 

omni5 Feeding rate of omnivore upon 
detritus 

omnivore*detr*0.0176 

detexcr Excretion rate of detritivore (0.1*detritivore)++((IF (waterlevel<10) THEN (waterlevel*detritivore/3) ELSE 
(detritivore/3))) 

omni4 Feeding rate of omnivore upon 
detritivore 

0.04*(detritivore-0.1)*(0.1*omnivore)/(detritivore+1) 

para5 Parasitization rate of 
parasite/Parasitoid upon detritivore 

detritivore*para*0.00001 

rdetri Respiratory rate of detritivore 0.09*detritivore 
gr Grazing rate of herbivore upon 

producer 
IF (producer>30) THEN (0.4*herbivore*(producer-1)/(2+producer)) ELSE (1) 

rz Respiratory rate of herbivore 0.125*herbivore 



 Ecology, Economy and Society–the INSEE Journal [104] 

omni2 Predation rate of omnivore upon 
herbivore 

0.04*(herbivore-0.1)*(0.2*omnivore)/(herbivore+1) 

para2 Parasitization rate of 
parasite/parasitoid upon herbivore 

herbivore*para*0.00001 

input Nutrient input into system from out-
source 

(nutin*qv)++((IF (waterlevel<10) THEN (waterlevel*nutin/3) ELSE (nutin/3))) 

upt Nutrient uptake rate by producer (IF (nutr>0.2) THEN (1.0*producer*(nutr-1)/(5+nutr)) ELSE (0))+((IF (waterlevel<10) 
THEN (waterlevel*nutr/3) ELSE (nutr/3))) 

outn Nutrient outflow rate from system qv*nutr 
omni1 Grazing rate of omnivore upon 

producer 
0.04*(producer-0.1)*(0.2*omnivore)/(producer+2) 

para4 Parasitization rate of 
parasite/parasitoid upon omnivore 

para*omnivore*0.00001 

romni Respiratory rate of omnivore 0.02*omnivore 
para1 Parasitization rate of 

parasite/parasitoid upon producer 
para*producer*0.00001 

rpara Respiratory rate of 
parasite/parasitoid 

0.001*para 

out_ph Outflow of producer from system producer+qv+0.1*producer 
rpro Respiratory rate of producer 0.02*producer 
qv Outflow constant 0.05 
nutin Nutrient input into the system from 

out-source 
40 

producer Autotrops in the system 35 
para Parasite/parasitoid in the system 1 
omnivore Omnivore in the system 1.5 
nutr Nutrient in the system 1.6 
herbivore Herbivore in the system 10 
detritivore Detritivore in the system 0.6 
detr Detritus in the system 16 
carnivore Carnivore in the system 1 



[105] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

APPENDIX 2: Equations Used in the Construction of the Model 2 

Equations No 

 

8 

Inflows  

 

8.1 

 8.2 

 8.3 

Outflows  

 8.4 

 8.5 

 8.6 

 8.7 

 

9 

Inflows  

 9.1 

 9.2 

 9.3 

 9.4 

 9.5 

Outflows  

 9.6 

 

9.7 

 9.8 

 

10 

Inflows 10.1 



 Ecology, Economy and Society–the INSEE Journal [106] 

Equations No 

 

10.2 

Outflows  

 

10.3 

 10.4 

 10.5 

 10.6 

 10.7 

      (11) 

11 

Inflows  

 

11.1 

Outflows  

 

11.2 

 11.3 

 11.4 

 11.5 

 11.6 

 

12 

Inflows  

 

12.1 

 

12.2 

Outflows  



[107] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 

 
 

Equations No 

 

12.3 

 12.4 

 

13 

Inflows  

 13.1 

 13.2 

 13.3 

 13.4 

 13.5 

Outflows  

 13.6 

 13.7 

 13.8 

 13.9 

 

14 

Inflows  

 14.1 

 14.2 

 14.3 

 14.4 

 14.5 

Outflows  

 14.6 

 14.7 



 Ecology, Economy and Society–the INSEE Journal [108] 

Equations No 

 

15 

Inflows  

 

15.1 

 15.2 

Outflows  

 

15.3 

 

15.4 

 15.5 

 15.6 

 15.7 

 15.8 

 16 

 

17 

 18 

 19 

 20 

 21 

 

22 

 3 


