After a debate that lasted for several decades, environmental considerations have been accepted as an essential -and necessary- part of the assessment of energy conversion systems. As of the time of this writing, several paradigms are in place to identify and quantify the “anthropogenic environmental impact,” and major Environmental and Governmental Agencies shelved the crude “emission level control” of the ‘80s to prescribe comprehensive and detailed analysis of the local and global implications of the interactions of anthropic processes with the biosphere (both locally and at large). In fact, the large majority of current regulations go well-beyond the simple “assessment of ecological damage” (intended simply as “pollution”). Quantifiers of such interactions, known as Environmental Indicators (EI in the following), have been and are still being proposed and applied to different systems under diverse scenarios and with different system boundaries, to provide a sufficiently accurate and reliable decision support basis for decision makers. The definition of a reliable and robust EI invariably poses some problems: for example, some of the most popular EIs are based on a restricted number of control parameters (quality of air, public health, social equity, etc.) and offer only an incomplete measure of the actual environmental impact. Moreover, most of the “sustainability” indicators currently adopted in Biosciences are not rooted on rigorous thermodynamic principles and often require rather arbitrarily “weighed” decisions on the part of the analyst, which may generate confusion among final users. This paper proposes a method to construct thermodynamically correct Environmental Indicators to rigorously address the problem of “sustainability.” Approaching the problem under this point of view, it becomes immediately clear that if the problem is tackled starting from fundamental principles a thermodynamic redefinition of the very concept of sustainability is necessary. In fact, Second Law negates the possibility for any open and evolving system to maintain itself in a “sustainable” state without availing itself of a continuous supply of low-entropy input^1,2. Therefore, the idea that “future generations” may successfully “satisfy their needs” (UN, 1987) while their resource base is irreversibly dwindling leads either to the enforcement of an untenable Malthusian level of numerosity control of the population (Sciubba and Zullo, 2009) or to an extreme degree of “prosperous de-growth” (Galor and Moav, 2001; Martínez-Alier et al., 2010) in all likeliness unacceptable by our progeny.

The modern concept of environmental sustainability dates back to the early ‘60s, when the then dominating view of technology-driven economic growth came under the fire of a generic criticism based on the perception that the quality of the environment is closely linked to economic development. Admittedly, in those years academic support for the “steady state” economy (i.e., no-growth in mass throughput) was less than lukewarm, but as public opinion became strongly involved through the environmental movements, public Agencies and Governments became actively involved, promoting new procedures and issuing new regulations (Paul, 1998). Perhaps the most important step was the 1968 foundation of the Club of Rome), followed by their publication in 1972 of Limits to Growth (Club of Rome, 1972). Other initiatives followed, like the establishment of the Worldwatch Institute in 1975, and finally the term sustainable development was officially coined by the United Nations Commission (usually referred to as the “Brundtland Commission” from the name of its president, Gro Harlem Brundtland). It must be mentioned that the Commission report was largely based on the suggestions formulated in the previous decade by Daly and Costanza (Daly, 1977, 1996; Costanza et al., 1997). This 1987 report (UN, 1987), Our Common Future, contains the (too) often cited definition of “development which meets the needs of the present without compromising the ability of future generations to meet their own needs.”

In the last four decades, the concept was further developed, leading to the United Nations Millennium Declaration (September 2000 in Rio de Janeiro) which set out eight “United Nations Millennium Development Goals” (MDG), to be achieved by 2015, committing world leaders to fight poverty, hunger, disease, illiteracy, environmental degradation, and discrimination against minorities (UNEP, 1992). Following suit, the World Summit on Sustainable Development (WSSD, Johannesburg 2002), produced the first political declaration (the “Johannesburg Plan of Implementation”) setting global goals and targets on the access to water, sanitation and modern energy services, on increasing energy primary-to-final use efficiency, on the exploitation of renewable energy sources, on establishing and maintaining sustainable fisheries and forests, on the enforcement of a more accurate monitoring and management of chemicals, etc. The rationale here was that of decoupling environmental degradation from economic growth and of achieving “sustainable patterns of consumption and production.”

The term “eco-development” had already appeared in the UN Environment Program review in 1978, and its most important feature was the recommendation that environmental and developmental ideas be considered concurrently. The paradigmatic definition of the Brundtland Commission elaborated on this approach, but it contains two rather obscure points that need clarification:

Some scholars correctly observed already in those early years that it is exactly the vagueness of the definition of the “sustainability issue” that made it palatable to decision makers worldwide: it is becoming painfully clear today that “sustainable development” is something everyone can agree to, but that merely positing it does not provide exact guidelines on how to achieve its goal.

Today, we are faced with practical questions such as: What does sustainable development really mean for different communities? How can we put the concept into practice? How do we know if we are transitioning toward a sustainable world? These questions demand for a measure of environmental effects, both at local and global scales, and this is why current “environmental policy declarations” make explicit use of both local and global EI, defined (EPA, 2008) as “… a numerical value that helps provide insight into the state of the environment or human health… Indicators are developed based on quantitative measurements or statistics of environmental condition that are tracked over time.” They “… can be developed and used at a wide variety of geographic scales, from local to regional to national levels. By monitoring the environment using indicators … (it is possible to)… share meaningful environmental information with the public, and ensure that high-quality environmental decisions are made.”

Another problem is that the concept of sustainability is not only rather fuzzy (a criticism that nowadays most schools of thought agree upon) but that it also lacks a rigorous scientific foundation. The very idea that a chemically and thermally non-homogeneous open system of constant total mass may be “sustainable” tout court (i.e., that it may remain in its -possibly dynamic- state “forever”) conflicts with the dictates of the Second Law of Thermodynamics (Valero-Delgado et al., 2011). The main problem is that the currently accepted definitions of “sustainability,” “sustainable development,” “sustainable growth” etc. make implicit or explicit recourse not only to exact physical sciences (to which thermodynamic laws apply), but also to several different branches of knowledge like Economics, Social- and Political Sciences, all of which are intrinsically ruled by “value judgements” that cannot be easily falsified in Popper's sense³ and are in general axiomatically posited⁴. The (too!) often published “three pillars paradigm” (Figure 1) that asserts that the concept of Sustainability stems out of three fields of knowledge, Social, Economics and Environmental sciences, has been strongly criticized by influential scholars (Thompson, 2017; Purvis et al., 2019), but the idea is so catchy and so heavily publicized, even on public media, that most decision makers take it for granted.

The approach taken in this paper is in this perspective frankly “reductionist.” When addressing problems like “rational resource exploitation” and “equitable resource distribution”, the role of Physical Sciences is predominant: it is rather clear that a resource-based metrics is less biased and must be favored, and as a consequence the non-thermodynamic attributes of a “sustainable system” ought to be considered at a “second step level” and be carefully reformulated in terms of their primary resource equivalent. In such a perspective, it is clear that the inherent fuzziness of the current concept of “sustainability” is due to the neglect of the fundamental separation between its thermodynamic⁵ basis, that should be the plinth on which possible “pillars” rest, and the socio-economic one, which falls under the domain of different branches of science, is measured by different quantifiers, and ought to consider the thermodynamic part as a preliminary filter and therefore abandon the glorious idea that a “sustainable state” be attainable by a simple resource re-allocation.

Environmental Indicators are used at different aggregation levels in industrial, economic, social and environmental studies as a synthetic and significant way of “representing reality.” They facilitate a concise and reproducible information exchange between specialists (scientists at large) and non-specialists (herein collectively denominated “decision makers,” including in this term the public opinion). As their name implies, EIs ought to be quantifiers that measure the “environmental quality” at a local, industrial, regional, national or global scale and should be used to directly compare -and possibly integrate- different scenarios. A careful examination of most of these quantifiers reveals that the problems lie in the link between the formulation of each indicator and the phenomenological model it subsumes. Combining some widely accepted inventories of necessary properties of an Environmental Indicator (Jackson et al., 2000; Dale and Beyeler, 2001; Gong and Wall, 2001; Sciubba, 2013) we can extract a useful conceptual list of evaluation criteria:

In conclusion, the EI that we shall consider in the present study are a) purely thermodynamic; b) resource- based; c) global; d) exergy-based. The fourth attribute is justified by the well-established record of results brought about by the adoption of exergy in the analysis of technical systems (Dewulf et al., 2008).

The fundamental idea of this study is that a human society can be modeled as a (non-equilibrium) thermodynamic system (Demirel, 2007; Lebon and Jou, 2008). In such an approach, the relationship between a “human society” (H) and “the environment” (O) can be quantified using thermodynamic tools. Since diverse forms of energy flows are involved that cannot be simply algebraically combined (like for instance chemical energy, thermal energy, human labor etc.), and since it is rather obvious that “thermodynamic sustainability” is inextricably linked to the Second Law, we shall use without further justification exergy⁶ as the sole quantifier for our considerations (for a definition of exergy and a detailed discussion on its properties and applications, see for example (Fratzscher, 1965; Moran, 1982; Szargut et al., 1988; Wall, 1997; Wall and Gong, 2001).

Natural systems are complex and display non-linear behavior, because they possess self-regulating mechanisms consisting of a vast web of positive and negative feedback processes that operate concurrently and regulate the carrying, regeneration, and assimilation capacity of the respective systems. As stated above, they are clearly in “non-equilibrium”: how does the model of Figure 6 account for situations in which, for instance, H “grows” in time and is non-homogeneous? To get some insight, let us analyze the term Ė_acc,H that represents the “accumulation” (embodiment) of exergy into H: such an embodiment can be material (mined ores are transformed into artifacts) and/or immaterial (exergy extracted from O is consumed in the production processes). Equation (2c) can be recast in a more useful form by assuming that the biodegradation effort be proportional to the exergy of the waste flows:

Where κ is a (not necessarily linear and not necessarily scalar) function of the respective thermodynamic states of O and H and of the intensity of the waste flux: κ = κ(O, H, Ė_w,H). The balance for H becomes:

We can now use equations (2d) and (4) to assess the thermodynamic sustainability of the open system (O∪H):

Which sets a global upper limit to the accumulation rate Ė_acc,H.

Equations (2–5) constitute therefore a suitable, and global, model for assessing the thermodynamic sustainability of a human society interacting with an open environment. On this basis it is therefore possible to derive proper global indicators. In fact, the above representation of the composite system O∪H enables analysts to apply standard concepts of exergy analysis and define at least three different forms of “efficiency”: an “intrinsic efficiency” of H is obtained by calculating the ratio of the useful product of all processes enacted within its boundaries (Ė_acc,H) to the total incoming exergy flux Ė_in,H:

The reciprocal of η_H, c_H, is an “exergy cost” that measures the exergy rate [in W] needed to produce a unitary rate of accumulation:

Both η_H and c_H are indeed global EIs, because they neither explicitly nor implicitly relate to “local” conditions around or within H, and relevant, because they provide a quantitative measure of how well H “exploits” the exergy flow it extracts from O. H could increase its accumulation capability either by reducing Ė_δ,H (i.e., improving its internal processes to reduce irreversibility and therefore increase η_H and decrease c_H) or/and Ė_w,H (i.e., reducing the unused portion of Ė_in,H released as waste into O by implementing more effective recycling procedures).

If we consider that the environment uses a portion of its exergy supply (Ė_B) to buffer the waste it receives from H, another measure of efficiency can be defined:

This appears to be a better efficiency indicator, because it accounts for the gross exergy input into H and includes the “hidden” load placed by H on the environment by forcing some biodegradation action. Its reciprocal, the cost c_H,ext, measures the exergy Watts needed to produce a unitary rate of accumulation including the environmental “service” provided by B:

From the “combined system” point of view the useful exergy flux available for the accumulation in H is though Ė_in − Ė_out, so that a global system efficiency can be defined:

Its reciprocal, the cost c_H∪O, measures the gross exergy Watts needed to produce a unitary rate of accumulation, i.e., a global “production cost”:

The above indicators provide a global measure of the ability of H to interact with O and exploit a given portion of the overall available “fuel,” defined as the difference between the incoming (low entropy) exergy flux and the (high entropy) portion re-radiated by O. The cost defined by equation (11) represents the total amount of primary exergy Ė_in − Ė_out needed to “produce” a unit of accumulated exergy Ė_acc,H: this is the “thermodynamic impact” of H's growth on the environment.

The method can be extended to more than one system interacting with O and also easily manipulated to include interactions between several systems H₁, H₂…: notice that the above defined costs are time dependent and can be used to assess the evolution of the interplay between systems and the environment and of the state of the combined system O + H₁ + H₂ etc.

Notice also that a continuously decreasing value of either one of the above efficiency indicators in time (or, which is equivalent, an increase in the costs) signals a situation in which H (or indeed the combined system O∪H) may be on a thermodynamically unsustainable path: in fact, Ė_acc,H = 0 is the limit case of “steadiness” (survival with no growth) and Ė_acc,H < 0 indicates negative growth, an obviously unsustainable condition. In conclusion, both the efficiency indicators and the costs are proper EI.

While the above exergy-based description is perfectly suitable to evaluate the primary resources (solar irradiation, water, air and material taken directly from some natural reservoir in the environment surrounding the system), exergy per se is not a proper quantifier for secondary resources, i.e., resources on which some “work” or “action” has been performed by a system to bring them to the state at which they cross the control surface. The correct measure of the “exergy cost” of such pre-treated resources is the total amount of natural resources directly and indirectly expended in their transformation from the “state 0” to the state in which they cross the boundary of the system, measured in units of exergy. This is their embodied exergy content¹⁰. Quite clearly, the identification of the production chains (the direct one and all of the indirect processes that generate the individual externally manufactured inputs) and the definition of the limits for the indirect exergy supply (i.e., the proper identification of the relevant control volume) are crucial issues in such an approach.

The embodied exergy content of a product or service can be calculated following, for instance, the Cumulative Exergy Content CExC (Szargut et al., 1988), the Thermo-Ecological (or Exergo-Ecological) Cost TEC (Szargut, 1995, 1999, 2005) or the Extended Exergy EEA (Sciubba, 1998, 2001; Colombo et al., 2013) methods. All three methods maintain that any external intervention that adds or subtracts exergy from a stream before it crosses the control surface can be accounted for in terms of expended primary exergy. Since the terms in the balance equations (2) through (5) are completely quantifiable and homogeneous, the expenditures related to these external interventions can be algebraically added. The most popular methods used to derive exergy-based EIs, namely, the CExC, the TEA and the EEA, are presented and compared in the following sections, with the purpose of illustrating the difference between their respective EIs and to assess their commensurability (i.e., the existence of a procedure to convert one into the other). The three procedures are examined separately, with reference to the respective “control volumes” depicted in Figure 7 (CExC), Figure 8 (TEA) and Figure 9 (EEA)¹¹.

Both the tec and the eec are genuine resource consumption quantifiers, since both express a measure of the “environmental load” placed on system O by activities originating in H. They are obviously correlated (a production line with a minimal tec is likely to also have a minimal eec), and thus it is interesting to investigate whether the correlation admits of a mathematical expression.

For the sake of comparison, consider a process that produces N units/(unit time) of a commodity and emits m kg of CO₂ per unit. Let us also assume that the product exergy e_P, the exergy of the discharges e_D, the amount of non-renewables Ė_NR and the exergy destruction rates are known. The ee_c is:

In the case of multiple products, proper allocation rules are suggested in (Sciubba, 2001; Colombo et al., 2013): they are formally the same as those adopted in TEC, but the structure of equation (16) allows for a more disaggregated account for the individual contributions (Labor, Capital and Environmental Remediation Cost), thus making the allocation easier. A perusal of equations (15, 16) suggests that the numerical values emerging from the calculation of the cexc+tec and ee_c are incommensurable, which is confirmed by a simple virtual experiment. Consider the reasonably realistic “sustainable” scenario described below:

Under the above scenario, equation (15) simplifies to:

In light of the above considerations, we can now introduce a novel indicator, the Exergy Footprint ExF, defined (Sciubba, 2012) as the amount of primary exergy (in J) globally consumed over the life of a commodity, including material, energy, labor, capital and environmental remediation costs and calculated on a life-time basis.

The ExF is the integral in time of the eec, and it is clear that the Second Law places a lower limit to its numerical value: even if we could adopt a “perfect recycling,” some external exergy source would be necessary to sustain the process and compensate for the exergy destruction. We recover here the idea that thermodynamic sustainability (eec = 1 when calculated for the whole Society) is impossible: therefore it would be more proper to speak of a “degree of unsustainability,” ξ = (eec-1)/eec.

The ExF provides useful -and unique- information at several levels:

The current concept of “sustainability,” though almost acritically accepted by media and decision makers, is far too vague to be amenable to practical and meaningful scientific use. In a thermodynamic sense, a closed system is never sustainable (unless it is at equilibrium, i.e., “dead”), and an open one may be sustainable or not depending on whether the exergy input rate is higher (or not) than the sum of the exergy destruction and accumulation rates within the system, augmented by the exergy expenditure required by the environment to buffer the effect of the effluents. It is therefore important to realize that there are two facets to a “sustainable development”: the first is of thermodynamic nature, governed by the relevant system equations described in this paper, and the second described by socio-economical indices, whose interpretation is outside of the bounds of Thermodynamics. As for the former, it is convenient to adopt exergy as a general quantifier, because it not only attributes a thermodynamically correct value to any type of flux, but also directly relates irreversibility to unsustainability: reversible processes are intrinsically sustainable (too bad there is none known in the Universe!).

It is rather clear that the socio-economical interpretation must be supported by the thermodynamic one, in the sense that if a system “uses” the incoming exergy flow in a way that leads to a total net depletion rate of (fossil or renewable) exergy sources, no societal organizational form can survive in the long run unless new exergy inputs are provided at a sufficient rate. It is true that the specific form of the societal organization may affect -ceteris paribus- the exergy depletion rate, but this does not imply that such a “minimum exergy consumption” society may be acceptable from an ethical point of view: this decision implies a value choice and is outside of the realm of Thermodynamics. Studies that do not separate these two issues are therefore bound to reach wrong and misleading conclusions.

Indicators of the “resource efficiency” of a system (be it a production line, a natural species, a human settlement, an entire nation) can be defined only in the thermodynamic system logic and at the largest system physical scale: they are termed here “global.” It is important to realize that “local” indicators are completely legitimate, but since they are by definition concerned either with a set that generally includes non-thermodynamically relevant quantities or with a limited subset of the state variables of the system, they cannot be taken as genuine indicators of the degree of sustainability as formulated above.

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.

The author confirms being the sole contributor of this work and has approved it for publication.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.