An Exergy-Based “Degree of Sustainability”: Definition, Derivation, and Examples of Application

Abstract

The work presented in this paper is a contribution to the practical implementation of the “sustainability” concept, which is tightly connected with “resource thriftiness”, i.e., with reduction in the anthropic extraction of the irreplaceable supplies of fossil materials—ores and fuels—contained in the Earth’s crust. The saving is tied with “environmental conservation”, which is another concept embedded in the definition of sustainability. This paper starts from the assumption that the best measure of “resource consumption” is the total equivalent primary exergy extracted from the biosphere. The question is, then, while it is evidently correct to include social, ethical, and monetary matters into the definition of “sustainability”, what about the required resource consumption? To answer this question, the dynamic balances of a society represented as a thermodynamic system were examined to show that a “sustainable state” can be reached under two necessary conditions: first, the supply must consist only of renewable resources; and, second, the rate of such a supply must be higher than a certain threshold that can be attributed a physical significance. The procedure outlined in this paper leads to a rigorous definition of a society’s “thermodynamical degree of sustainability”, which is based solely on the primary renewable and non-renewable exergy inputs, as well as on the final exergy consumption. Some examples of applications to industrialized and non-industrialized countries are also presented and discussed.

1. Introduction: About the Definition of Sustainability

1.1. Preliminary Considerations

Despite extensive media coverage, even a superficial survey of the reports of governmental agencies and public and private institutions shows that the concept of ‘sustainability’ is often misunderstood or—worse—its application is misdirected. It is, therefore, important to define a systematic procedure for a correct and rigorous definition of both “sustainability” and of “sustainable development”.

1.2. Some Pitfalls in the Definitions

A compilation of some authoritative definitions of “sustainability” were collected, as shown below.

• United Nations Brundtland Commission: “Sustainable development means meeting the needs of the present without compromising the ability of future generations to meet their own needs”. But what are the needs of future generations, and why are we qualified to establish them?
• European Environmental Agency: “Sustainability is about meeting the world’s needs of today and tomorrow by creating systems that allow us to live well and within the limits of our planet”. But who decides what “living well” means? In other words, who can impose some “globally valid life standards”?
• US Environmental Protection Agency: “To pursue sustainability is to create and maintain the conditions under which humans and nature can exist in productive harmony to support present and future generations”. This is a better definition but still dangerously vague as one possible way to become “sustainable” would be to drastically reduce the world’s population…
• Cambridge Dictionary: “The quality of causing little or no damage to the environment and therefore being able to continue for a long time”. Still too vague of a definition.
• Encyclopaedia Britannica: “Sustainability [is] the long-term viability of a community, set of social institutions, or societal practice. In general, sustainability is understood as a form of intergenerational ethics in which the environmental and economic actions taken by present persons do not diminish the opportunities of future persons to enjoy similar levels of wealth, utility, or welfare”. Good formulation, but the questions posed in Points (i) and (ii) stand.
• Alberta University: “Sustainability means meeting our own needs without compromising the ability of future generations to meet their own needs. In addition to natural resources, we also need social and economic resources. Sustainability is not just environmentalism. Embedded in most definitions of sustainability we also find concerns for social equity and economic development”. Probably the most crisp definition of the list but still vague.

An interesting discussion about sustainability and related indicators is provided in [1], but it was not included in the analysis of the exergy considerations. More recently, Kardung et al. [2] proposed a conceptual framework for analyzing the development of the EU bioeconomy and identified a set of possible indicators (none of which were related to exergy): such a pressure/resilience approach is evidently important for a sustainability analysis, and the work discussed below can contribute to expand this kind of methodology and provide it with a more rigorous physical basis.

1.3. Exergy and Sustainability

Exergy is defined as the maximum useful work that can be extracted from a system as it comes into equilibrium with its environment while only interacting with it [3]. A symmetric definition, relevant to the topic discussed in this paper, reads as follows: “Exergy is a measure of the minimum useful work that must be provided to the set ‘system + environment’ when the system, originally in equilibrium with its environment, is brought to a different state”. Notice that “work” here indicates the adiabatic work obtained by, for example, raising or lowering a weight against a body force field. Unlike energy, which is always conserved, exergy is always destroyed, except for ideal isentropic processes, due to irreversibilities.

Exergy analysis (ExA) is widely employed to identify and assess the sources of irreversibility in real industrial processes, and its success as an analysis and optimization tool has spawned a new branch of engineering economics, namely Thermo-Economics (TE), which links the installation and operation costs of a technological chain to the exergy efficiency of its components and to the exergy flows connecting them [4,5,6]: in its modern standard formulation [7,8], TE is commonly regarded as the most advanced process analysis method in the energy conversion arena. Since both ExA and TE can be formulated in such a way as to calculate the exergy “used” to generate a commodity—and it is clear that, in this perspective, the higher the exergy efficiency, the lower the resource use—it is tempting to link ExA to sustainability. In the last few decades, there have, indeed, been several attempts to link the two concepts both qualitatively and quantitatively. Coatanea et al. [9] proposed to use the exergy destroyed in a process to measure its environmental sustainability, and they presented quantitative applications to realistic energy conversion systems. Diaz Balterio et al. [10] introduced an Index of Sustainability for natural (i.e., non-anthropic) systems, and they then proposed to extend it to reach a balance (a constrained optimum) between an engineering solution of ‘‘maximum aggregate sustainability’’ and an ecological solution of ‘‘most balanced sustainability’’. Diaz Mendez et al. [11] expanded on Coatanea’s approach and proposed to quantify environmental sustainability by the cumulative exergy destruction of a process. Kharrazi [12] compared several approaches to concoct a measuring scale for sustainability, and they concluded that if the quantifier measures the amount of the available resources that are used and the efficiency of their conversion, all other dimensions of the sustainability concept (resilience, social impact…) are lost. Moreover, this approach fails to establish a quantitative link between an improvement of efficiency and the corresponding increase in the sustainability of a system. On the other hand, a purely ecological-oriented approach, while highlighting properties like resilience and robustness to external pressures, cannot properly quantify the consumption of available resources. Maes et al. [13] performed an extensive analysis of bioenergy processes and concluded the following: “within the context of sustainability assessment of bioenergy, exergy is a suitable metric for the impacts that require an ecocentric interpretation, and it allows aggregation on a physical basis. The use of exergy is limited to a measurement of material and energy exchanges with the sun, biosphere and lithosphere. exchanges involving services or human choices are to be measured in different metrics”. Their conclusion is reported verbatim here in view of the quite different conclusions presented in Section 1.4. Romero and Linares [14] tried to pinpoint the merits and drawbacks of some of the exergy-based methods used to quantify sustainability: although their analysis is quite detailed and well organized, some of their conclusions are thermodynamically incorrect. On the basis of a previous proposal by Valero [15] to quantify the environmental load posed by an industrial system on the biosphere by the amount of exergy required to “restore” the extracted material to the same location and the same concentration, Whiting et al. [16] performed an in-depth analysis of this exergy replacement cost (ERC), and they concluded that it is not always granted that the use of “alternative, eco-friendly fuels” results in an improvement of the overall sustainability of a society. This is because the connections of the considered process with other sources, sinks, and processes constitute a strongly non-linear system whose response is not discernible a priori.

Badmus [17] proposed to directly correlate the exergy destruction with the sustainability of a fossil conversion process. His conclusions are acceptable only in the restricted frame of his analysis because the correlation he posits between “emissions” and “pollution” (=environmental degradation potential) is not measurable in terms of the exergy of the effluents.

Szargut [18] presented a remarkably detailed and rigorous analysis of the possible use of ExA to quantify environmental damage, but he encountered problems when trying to link the exergy of effluents to the “remedial cost”. An interesting proposal was put forth by Tsatsaronis and Morozyuk [19], who linked the “pollution indexes” provided by life cycle analysis to the exergy flows in a process: by applying the standard calculation of the exergy costs (i.e., of the primary exergy used to generate a certain flow) and weighing each flow with its LCA pollution index, he was able to attach a cumulative pollution index to each effluent.

The majority of the above approaches—as well as several other ones found in the literature, which are based on similar assumptions—are questionable under a physical point of view.

(1).

The assumption that the exergy content of a discharged stream is proportional to the environmental damage it generates is wrong. In fact, it is readily proved by a concurrent ExA and toxicity analysis that high-exergy discharges of non-toxic materials generate much lower impact than low-exergy discharges of toxic material.

(2).

It is true that an ExA describes only the thermodynamic facet of the problem, but the resource-based version of TE (especially the above-cited TEC defined by Szargut) can already internalize the environmental externality.

The real crux of the problem is then shifted to the question of whether social and economic issues must be handled by other systems of indicators or whether they can be connected in some way to the primary resource consumption.

Let us approach the problem from a different point of view: if a system can avail itself of insufficient resources, will it be able to evolve towards a sustainable state, or will it de-grow to a dead state? Conversely, assuming a system thrives on a large resource base, what are the conditions for it to evolve toward a sustainable state? A moment’s reflection (and with a brief excursus of the history of the rise and fall of civilizations) suggests that societal organization, welfare, and health management can originate only as “subsystems” within a society that is sufficiently resource-rich to consume only a portion of its resource input to “survive”, making the surplus available for “growth” and “life quality”. This consideration leads to the main purpose of this paper: “sustainability” is a complex and multi-faceted concept that envisions material and energy use, social equity, welfare, conservation of the environment, etc., and it is likely that it can only be measured by a multi-dimensional indicator. But, for a society to exist and evolve, it is necessary to consider the dynamics of its resource use. If the available resource base is consumed “sustainably”, the society can thrive as long the resource base is sufficiently abundant; if the consumption is “unsustainable”, the evolution may lead to a—gradual or catastrophic—degrowth. Thus, the definition of a degree of sustainability based on thermodynamics is essential to assess future projections and scenarios.

1.4. The Exergy of “Growth”

Before discussing the definition of a thermodynamics-based degree of sustainability, it is important to clarify one point that was raised by the above-cited work of Kharrazi and Maes [12,13]: an ExA can provide information about the resource side of the cost, but monetary and social issues must be handled by different paradigms. The history of the development of exergy-based methods contradicts this argument as, already in the 1960s [4], ExA had been combined with engineering economics into a novel paradigm, Thermo-Economics, which could be used in two different “modes”: a monetary one, in which a monetary cost is attributed to the unit of exergy of each product; and a resource-based one, in which the unit of product exergy is attributed a cost in terms of the resource used to generate it. In 2002, Szargut et al. summed up 15 years of investigations on the use of exergy to assess ecological impact in a widely cited paper [18] that contained the definition of a quantitative indicator called the Thermo-Ecological cost (TEC), which is used to measured a sort of “exergy equivalent” of pollution costs (see also the Exergo-Ecological Portal: https://www.exergoecology.com/, accessed on 15 February 2025). The internalization of all the externalities (the labor, capital, and environmental remediation cost) was completed between 1998 and 2001 [20,21] with the introduction of the Extended Exergy Accounting method, which mutuates the exergy cost concept from TE, i.e., the ecological approach from TEC, and adopts a novel “costing” of the monetary expenses (capital flows and labor) based on the ExA of the country the process is located in (see also [22,23] for later developments).

In conclusion, ExA can be used to generate the “exergy flowchart” of a society and to formulate a costing paradigm that expresses the equivalent resource embodied in each final product. But environmental, social, and monetary issues cannot be included in the analysis unless additional stipulations are made (Extended Exergy Accounting). For the scope of this paper, however, it is possible to define the control volume in such a way that the country in question is considered a “black box” with its internal dynamics being lumped: this allows all considerations to be made using the exergy in- and outflows only. ExA has, indeed, seen several applications in the field of energy conversion systems and an increase in sustainable operation applications by a streamlining and improvement of the technological line [24,25,26,27,28,29], such that, in the present context, this “extension” to an entire country is only a change in scale. In conclusion, the argument of this paper, being that “there is no sustainability without survivability—and possibly growth”, is that an ExA will serve the scope.

1.5. The Degree of Sustainability

In a literal sense, a dynamic system (a human society specifically) is said to be in a “sustainable state” if the sum of its output P plus its internal irreversibility I are compensated by an external resource input R (be it material or immaterial). It is irrelevant at this point what quantifier we use to measure the flow of resources; however, a well-posed problem requires that the mass and energy balances be internally homogeneous and congruent. In the context of the present paper, the quantifier was “exergy”. In an interesting limit case (Figure 1b), the balance between internal “consumption” and external “supply” is exact,

R = P + I,

(1)

and the system can neither “grow” nor “shrink”. If R > P + I, then the system can make use of the extra resources to “accumulate” them, which can increase its output.

The important concept here is the rate at which resources flow in: as long as R(t) > P(t) + I(t), the system thrives, regardless of the fact that R be “renewable” or “fossil”. But, if we require that—as per the above definitions—the “sustainable” situation be valid for t → ∞, then, in this limit, Equation (1) must include only renewable resources.

The above considerations indicate the following.

• To properly represent the dynamics of a society, the four relevant parameters are the rate of renewable and non-renewable resource inflow R_r(t) and R_nr(t); the “output” E_out(t) of the society (goods, services, energy flows, and wastes); and its internal irreversibility E_δ(t);
• The five neo-classical economics “Production Factors” that measure societal output are Labor L, Capital K, Materials M, Energy En, and Environmental Cost O: if we adopt a monetary representation, each production factor must be attributed a corresponding monetary equivalent. This is, in fact, the motivation behind the attempts to “monetarize” the natural resources made by the supporters of the Natural Capital concept [30,31]. But, if P is expressed in monetary terms, then so must be R and I, and this leads to major problems in the proxification, which requires additional assumptions and leads to inconsistencies;
• The solution we advocate is to invoke Thermodynamics, i.e., to quantify all material and energy fluxes by their exergy equivalent value: this is immediately applicable to M, En, R and I but to extend it to L, K and O requires recurring to the above mentioned Extended Exergy Accounting, EEA. Since EEA uses the primary exergy flow as a “proxy”, all of the terms in Equation (1) are in units of power [W], with the explicit expression being the following:

  E_R(t) + E_NR(t) = P[K(t),L(t),M(t),En(t),O(t)] + E_d,

  (2)

  where K, L, M, En, and O are measured by their equivalent primary exergy, and E_δ is the exergy destruction rate;
• Modern human societies must be considered Very Large Complex Systems (VLCS), and they offer very few examples of thermodynamically sustainable instantiations (such as small tribes of hunters/gatherers, nomadic clans of shepherds, traditional fishermen’s groups, etc.): we can, thus, introduce a “degree of sustainability” to measure the “distance” between the current situation and our future target. This measure must be (1) standard; (2) homogeneous for all societies; and (3) variable from country to country and—for the same country—in time.

The reasoning that leads from the above simple considerations to the definition of an exergy-based degree of sustainability can be itemized as follows.

(a)

Assume the exergy input E_in,H consists (Figure 2) of renewable (E_R) and non-renewable (E_NR) resource flows: the exergy surplus E_S that can be used by the society to maintain itself (and possibly to grow) is given by

$$E_S=E_R+E_{NR}-E_{out}-E_{\delta },$$

(3)

where E_out is the rejected exergy flowrate, and E_δ is the irreversible exergy destruction;

(b)

Since the NR flows are, by definition, decreasing to zero in the limit of very long times, the sustainability conditions become

$$E_{NR}=0; E_{S,sus}=E_R-E_{out}-E_{\delta }.$$

(4)

(c)

For E_s,sus to be positive, we have

$$E_R\ge E_{out}+E_{\delta },$$

(5)

where the equality applies in the case of no-growth.

The physical meaning of Equation (5) is clear: for the system (=society) to thrive “sustainably”, the rate of renewable exergy supply from renewable sources must be equal to or higher than the sum of the exergy discharges plus the exergy destruction within the system.

There are three different scenarios.

(a)

ES + Eout + Eδ > ER: this system is not sustainable, and, if a portion ES-ER is not covered by non-renewable sources (ENR), the system enters de-growth [32]. Assuming that the deficit is indeed covered by non-renewable resources, let us now define a “Degree of Sustainability” DS as the complement to the unity of the ratio of the distance of ES from the available input ER divided by the total renewable input:

$$D_S=1-{\displaystyle \frac{{\mathrm{m}\mathrm{a}\mathrm{x}(E}_{R,}{E}_S+E_{out}+E_{\delta })-{\mathrm{m}\mathrm{i}\mathrm{n}(E}_{R,}{E}_S+E_{out}+E_{\delta })}{{\mathrm{m}\mathrm{a}\mathrm{x}(E}_{R,}{E}_S+E_{out}+E_{\delta })}}={\displaystyle \frac{{\mathrm{m}\mathrm{i}\mathrm{n}(E}_{R,}{E}_S+E_{out}+E_{\delta })}{{\mathrm{m}\mathrm{a}\mathrm{x}(E}_{R,}{E}_S+E_{out}+E_{\delta })}}.$$

(6)

The physical meaning of Equation (6) is also clear: if the total exergy input (E_S + E_out + E_δ) is higher than the available renewable resources, the society is not sustainable and D_S = 0. Otherwise, D_S measures the amount of E_S + E_out + E_δ that must be covered by non renewable resources, and the D_S is less than unity. In practical situations, the degree of sustainability can be increased by increasing E_R or, for a fixed E_R, by reducing E_out (minimizing the waste flows and optimizing recycles) and E_δ (increasing the conversion efficiency of the internal sectors). However, $D_S=1$ only for the ideal case of a reversible system with no exergy rejection;

(b)

E_S = 0, i.e., E_out + E_δ = E_R: the renewable resource inflow is just sufficient enough to cover the discharges and the system irreversibility. There is no surplus exergy rate available for development and growth: social, economic, and technological advances are highly unlikely.

(c)

E_S + E_out + E_δ < E_R: this is a “very virtuous” scenario in which the system is not only sustainable but has margin for a sustainable growth, and this is possible because the amount of ER-ES-Eout-Eδ can be still exploited. Definition (6) does not apply, but we can define another useful indicator, the “Margin for Sustainable Growth” MSG, as the ratio of the available extra input ER- ES divided by the total renewable input:

$$M_{SG}={\displaystyle \frac{E_R-E_S-E_{out}-E_{\delta }}{E_R}}.$$

(7)

No society in the world is known to be 100% powered by renewable resources, and the global input will generally be E_NR + E_R. However, Definitions (6) and (7) are independent of the amount of non-renewables because they do not affect the sustainability conditions given by Equation (4). Notice that M_SG → 0 as the renewable input is E_R → (E_S + E_out + E_δ).

Figure 3 provides an illustrative sketch of the behavior of D_S for an imaginary country in which the ratio E_NR/E_R decreases to zero between 2000 and 2050 and then remains zero for the next 50 years. From 2050 through 2100, the E_S is >0 and the country’s societal system grows exploiting the available extra resources.

A question arises about the correct calculation of E_S: under what form is this exergy “embodied” in the society? The exergy budget per se is incapable of assessing—for example—the quota of the net total input that must be allocated to the survival of the biosphere (via ecological damage remediation) or to the maintenance of the productive chain that “creates value” starting from pristine material or energy flows. This problem can be addressed by the Extended Exergy Accounting method, which can allocate E_S into its individual components like (the primary exergy equivalent of) capital and labor flows and environmental remediation costs. As this topic is outside the scope of this paper, the reader is referred to some previous work on this subject [21,23].

Once such a “thermodynamic sustainability” has been defined, we can introduce other parameters that are external to thermodynamics but are relevant to our perception of a “good & equitable life”, as anticipated in the 1995 work of Wall [33] and which was more recently summarized, for example, by the Human Development Index HDI (which account for life standards, health issues, education, equitable access to resources, etc.). Once we adopt a rigorous and highly selective quantitative indicator as a basis, then other non-thermodynamic indicators can be built upon it.

What is clear, however, is that if a society is not “thermodynamically sustainable”, it cannot be regarded as “sustainable”, even when subjected to an analysis performed by any other indicator.

1.6. Resource Cost as a Sustainability Indicator

The notion that “human societies thrive on physical resources and not on capital” [20] may seem iconoclastic, but it, in actuality, represents an extension of our understanding of nature’s evolution [34]: in fact, the substitution of the attribute “human” with “fungal” or “bacterial” or “insects” or “mammals” makes the above expression perfectly agreeable with scientists and lay people alike. Thus, we shall consider here that the primary exergy input into the country is the “cost” of the survival of the society. (Furthermore, since an accurate and complete exergy budget is available only for some of the countries considered in this study, this input was approximated by an “exergy factor” applied to the total energy input for which reliable data are available (see Section 4)). The results presented in this paper are based on the physical amount of exergy fed into the country, as provided by a standard ExA. Recall that the correct quantifier for the surplus exergy rate E_S is instead the extended exergy, such that the results presented in the next sections provide no indication of HOW such a society allocates this surplus. Since the database for the extended exergy input is limited to very few countries, and since this study is mainly methodological, it is important to present and discuss the procedure. Moreover, as further data become available, the results (and the analysis) can be updated, and an investigation of the ways E_S is allocated among social, economic, and environmental issues will be possible.

The exemplificative behavior displayed in Figure 3 allows for some general comments that illustrate the properties of D_S and M_SG.

(a)

2000–2015: the total exergy consumption of the country increases. Roughly 60% of the increase is covered by renewable sources. The D_S slowly grows from 0.5 to 0.6;

(b)

2015–2025: a recession lowers the exergy consumption. Both the renewable and non-renewable sources decrease but preference is given to a reduction in NR sources, such that the D_S increases to 0.7;

(c)

2025–2050: non-renewable sources are slowly phased out and a sufficient portion of renewables is installed to cover the exergy requirements. By 2050, the country is completely sustainable (D_S = 1), but since E_S + E_out + E_d = E_R, its growth margin is zero;

(d)

2050–2065: the increase in renewable sources exceeds the growth in the exergy consumption. The M_SG increases from 0 to about 0.25;

(e)

2065–2100: the supply of renewables remains constant, but it is still in excess of the country’s exergy consumption. The M_SG decreases slightly to about 0.15.

2. Material and Methods

For some of the countries analyzed here, reliable data for the primary exergy inflow E_in are not available: in doubtful cases, the value was derived by assigning an exergy factor f_ex [35] to each individual primary energy source. An exergy factor represents the exergy content of a unit of energy, and it is evidently dependent on the type and physical status of a material, as well as on the type of energy. (A typical textbook example is the exergy factor of a quantity of thermal energy Q available at a temperature T_Q > T₀, which, in this case $f_{ex,Q}=Q[1-{\displaystyle \frac{T_0}{T_Q}}]$,)

$$E_{in}=\sum f_{ex,j}{En}_j,$$

(8)

where En_j are the individual resources (fossil or renewable) in kWh/yr.

A similar approach was adopted to calculate the final exergy use E_S: the final energy use, as well as its allocation by source, was known, and the same formula was also used. The values of f_ex are shown in

Table 1. The Szargut–Styrylska exergy factors used in the calculations.

Resource	Oil	Gas	Coal	Nuclear	Electricity	Hydro	Solar	Wind	Biomass
fex = ex/en	1.07	1.04	1.1	1.05	1	1	0.94	1	1.05

: “ex” and “en” represent the unit flowrates of exergy and energy, respectively (measured in W).

The sum E_out-E_δ was calculated from Equation (2):

$$E_{out}+E_{\delta }=E_R+E_{NR}-E_S$$

(9)

The degree of sustainability D_S and the margin for sustainable growth M_SG were calculated from the definitions of Equations (6) and (7), respectively.

3. Sustainability Assessments for Both the Current and at 2050 for Some Countries

The calculations were made for a “current” year for which reliable data were available and for the projected 2050 scenario for each country. The results are summarized in

Table 2. The thermodynamic degree of sustainability for different countries.

Country and Year	ER, TWh/yr	ENR, TWh/yr	ES, TWh/yr	DS
Brazil, 2023	1980	2110	2920	0.51
Brazil, 2050	3500	2030	2830	0.66
China, 2024	7080	43,700	35,000	0.15
China, 2050	14,000	31,500	36,900	0.32
France, 2025	362	2270	1680	0.14
France, 2050	1960	1080	1300	0.65
Ghana, 2021	56.5	89.6	110	0.41
Ghana, 2050	861	110	773	0.89
India, 2025	1980	11,400	2470	0.16
India, 2050	6300	20,700	8470	0.25
Italy, 2023	349	1380	1470	0.21
Italy, 2050	1740	1850	791	0.88
Kenya, 2020	253	65.1	175	0.83
Kenya, 2050	359	65.9	280	0.86
Norway, 2020	198	163	344	0.57
Norway, 2050	263	92.3	223	0.75
Portugal, 2023	132	247	19.8	0.36
Portugal, 2050	159	188	111	0.88
Romania, 2023	163	268	308	0.40
Romania, 2050	169	185	241	0.49

.

Case-by-Case Preliminary Policy Implications

In spite of the above caveat about the reliability of the database, the comparison of the D_S and of the E_out + E_δ between today’s and the 2050 scenario provides some interesting insight.

Brazil’s projections [36,37] foresee a reduction in the final exergy consumption that, coupled with a 77% increase in the renewable share, increases the D_S but reduces the system conversion efficiency. This happens because the E_out + E_δ increases by almost 50%. This is a known effect: conversion from some renewable sources (sun, wind, etc.) are inefficient at the current technological state and will probably remain so.

The 2050 Chinese scenario still heavily relies on fossil resources, such that its D_S, even if it almost doubled in value, remains one of the lowest in an absolute sense: China is not going to become much more sustainable than today [38,39]. While this is in line with the National Energy Plan, it will lead to an unpleasant situation in which China will become—in absolute terms—the most-polluting nation.

For France [40], the radical shutdown of the fossil plants led not only to a five-fold increase in the D_S, but also to a corresponding doubling of the losses due to the large recourse (over 51% of the 2050 primary input) to solar and wind sources.

Despite an extremely ambitious transition plan that foresees a seven-fold increase in the final exergy consumption and leads to a doubling of its D_S, the level of losses for Ghana [41,42,43] remains almost unchanged due to its strong recourse (33% of the 2050 primary input) to the biomass resource (whose availability is not guaranteed for the next two decades). Furthermore, the fossil sources increased in absolute terms.

India [44,45,46,47] seems to be on a similar path as China: its fossil resources will actually almost double from 2025 to 2050 but its D_S will remain low (other than for a small improvement brought about by the partial substitution of coal with biomass and solar sources). Again, this is not an encouraging scenario, especially concerning CO₂ emissions.

Italy [48,49] is basing its transition on solar and wind resources: its D_S is projected to quadruple, but the losses will also increase by a factor of 5 due to the intrinsic low efficiency of PV panels and wind turbines. Such a massive migration to PV and wind requires massive investments and will meet with the resistance of many “not-in-my-backyard” groups: in fact, the transition is already greatly behind schedule when it comes to the installation of PV plants (see the MW_p installed vs. those prescribed by the National Energy Plan as of 2025).

Kenya [50,51] will slightly increase its D_S and reduce its conversion efficiency by virtually substituting all its fossil sources with solar electricity. As for Italy, such a transition plan would require immense investments that may stress the country economic system. It is doubtful that the necessary infrastructure will be put in place according to schedule.

Norway [52] will replace 50% of its fossil plants with hydro and wind plants, thus increasing its D_S but also its losses.

Portugal [29,43] will double its D_S by switching to solar and wind sources, reducing its fossil sources by a factor of six. The fact that its losses decrease, however, is not in line with the known lower efficiency of the substitution; as such, the available data may be incomplete or partly incorrect.

Romania [53,54] plans to increase its D_S (with a small penalty about the losses) by reducing its final exergy consumption, i.e., streamlining its conversion chains. Natural gas substitutes for coal and oil, as well as an increase in wind, hydro, and solar sources, makes up for a corresponding reduction in biomass use. Global conversion efficiency is expected to decrease.

4. Conclusions

Sustainability indicators are measures that are used to assess the long-term viability and impact of practices, policies, and systems in environmental, social, and economic contexts. They are intended to be part of the decision tools that track progress toward sustainability goals and provide insight into the health of ecosystems, communities, and economies. In general, these indicators aim to evaluate how well current actions are aligning with the principles of sustainable development, which seeks to balance ecological protection, economic prosperity, and social equity.

The basic objection to the current interpretation of “sustainability” is purely thermodynamic: if a (natural or anthropic) system cannot avail itself of a sufficient amount of primary resources, it cannot survive. There are several examples in paleobiology (and, unfortunately, in contemporary biology also) that show that when a species is deprived of an excessive portion of its resource inflow, it either modifies its biological configuration (i.e., evolves) to adapt to the new situation or it becomes extinct. The claim here is double: First, there is the convenience of considering human societies as thermodynamic systems and of quantifying their resource and final commodities flows by their embodied exergy. Second, the aim is to introduce a fundamental postulate, i.e., an anthropic system can only reach a “physically sustainable” state if a well-defined dynamic balance between inputs and outputs is maintained. These physical considerations lead to the definition of a “thermodynamic degree of sustainability”, which quantifies how far from physically sustainable state a system is: the sole condition is that the rate of the exergy inflows is higher than the sum of the exergy outflows (rejections and discharges) and the exergy destruction. Only if this condition is satisfied can the excess exergy rate (E_S in this paper) be exploited by the system to survive and, if possible, grow. It is easy to see that when this condition is not satisfied a country cannot survive: it will de-grow until the thermodynamic survivability limit is again reached. In other words, when resource inflow falls below a certain limit, all sustainability indicators based on environmental, social, economic, or institutional consideration are not applicable anymore since no survival is guaranteed unless substantial societal changes take place.

Based on this approach, the exergy-based degree of sustainability of several contemporary countries was assessed for their current status and for the projections to 2050, and the results shed some interesting light on this complex issue.