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List of definitions (click on the words for direct access)

➵ Alternative energy source(s)

A primary energy source claiming it has the potential to become a significant contributor (superior to 20 per cent) of the overall market in the local, regional, national or global energy supplies. The potential and quality of an alternative energy source can be assessed by performing an integrated assessment of its viability, feasibility and desirability. Examples of technologies claimed as being alternative energy sources are nuclear power, biofuels, photovoltaic power, wind power, hydrogen, etc. Currently the search for alternative energy sources is motivated by the depletion of affordable fossil energy resources.

➵ Benchmark

An indicator that serves as a standard or as point of reference by which other quantitative values may be measured or judged. In MuSIASEM a benchmark is an expected value describing one of the metabolic characteristics of a known type of socio-ecological system.

➵ Bioeconomic pressure (BEP)

An indicator of the material standard of living and hence of the 'desirability' of the metabolic pattern. The stronger the BEP in a society, the larger the share of production factors that ought to be allocated to the dissipative macro-compartment. It is formalized as the ratio of the total amount of production factors (fund and flow elements) of the society over the amount of production factors (fund and flow elements) allocated to hypercyclic compartments (the larger the share in the dissipative compartment, the smaller the share in the hypercyclic compartment).

➵ Desirability

Compatibility of the perceived performance of society with human expectations. It is one of the conditions for sustainability to be checked with the MuSIASEM approach (together with feasibility and viability).

➵ Dissipative compartment

The part of the society consuming the surplus of food or energy generated by the hypercyclic part. Using economic jargon we can say that it includes the compartments dealing with transaction activities (service and government) and final consumption activities (household sector).

➵ Endosomatic metabolism

Metabolic processes taking place inside the human body determining the conversion of different types of food energy inputs, i.e. food items, into end uses, i.e. physiological processes.

➵ Energy carrier (relates to ‘secondary energy’ in energy statistics)

Various forms of energy inputs required by the different sectors of a society to perform their functions. The characteristics of the energy carriers are defined by the characteristics of the energy converters (exosomatic devices) using them. Energy carriers are produced by the energy sector of a society by using 'primary energy sources'. Energy carriers include liquid fuels, electricity and process heat.

➵ Energy end uses

Useful tasks or work performed by the various sectors of society when converting energy carriers into applied power. Examples of end uses include moving goods, smelting iron, building a road and air-conditioning a room. The concept of end use implies the simultaneous presence of a given mix of production factors: both flow elements, for example energy inputs, wastes and materials, and fund elements, for example power capacity and human activity.

➵ Energy return on investment (EROI)

In semantic terms it indicates the ratio between the amount of energy output obtained by society in a process of exploitation of primary energy sources and the amount of energy input required for such an exploitation. However, it is impossible to implement the accounting of this indicator using a simple ratio among two numbers. In formal terms this assessment can only be obtained using data arrays and multi-level tables (to deal with the different quality of different energy carriers and existence of non-equivalent categories of accounting for energy flows).

➵ Exosomatic metabolic rate (EMR)

Measure of the exosomatic energy consumption per hour of human activity (measured in joules per hour). It can be calculated, across different hierarchical levels, for the various compartments making up a socio-economic system (EMRi = ETi/HAi) (in MJ/h). It can be measured in joules of energy carriers (then it is specific for the category of accounting, e.g. electricity, fuel, process heat), or it can be measured in joules of gross energy requirement (primary energy equivalent).

➵ Exosomatic metabolism

Technical conversions of different types of energy inputs (energy carriers) into end uses that take place outside the human body, but under direct human control.

➵ External constraints

They are determined by the existing favourable boundary conditions (availability of required inputs on the supply side and required sink capacity on the waste side), which are generated by processes beyond human control. Lack of favourable boundary conditions limits the possible forms of interaction of the metabolic system with its context and as a consequence limits the possibility of expressing functions inside the system. An external constraint is present when the limits to the expansion of the activity of the system are not determined by shortage of technical capital but by shortage of natural resources (supply of inputs or sink capacity for the dumping of wastes).

➵ Feasibility

Compatibility with external constraints. It is one of the conditions for sustainability to be checked with the MuSIASEM approach (together with desirability and viability).

➵ Flow elements

Those elements which are either produced (appear) or consumed (disappear) during the analytical representation. They reflect the choice made by the analyst when deciding "what the system does" and "how it interacts with its context". Examples of flow elements are relevant food, energy, monetary and material flows.

➵ Fund elements

Structural elements whose identity remains ‘the same’ during the analytical representation. They reflect the choice made by the analyst when deciding "what the system is" and "what the system is made of". Examples include humans associated with human activity, power capacity and land.

➵ Fund-flow (renewable) primary energy sources

Energy systems exploiting natural processes that can be considered stable in time, for example solar, hydro, wind and biomass, to generate energy carriers.

➵ Gross domestic product (GDP)

A flow defined as the added value generated by an economy (or economic sector) in one year, generally measured in US dollars (USD). GDP is taken from statistical sources.

➵ Gross energy requirement (GER)

A virtual quantity of thermal energy that is calculated using the partial substitution method to assess the total energy throughput of a society. This assessment is based on five different pieces of information: 1) the mix of energy carriers required as net supply by the ‘end uses’ of the various compartments; 2) the choice of accounting rules used to convert assessment referring to joules of electricity into assessments referring to joules of thermal energy; 3) the mix of primary energy sources; 4) the characteristics of the various processes of conversions; and 5) distribution losses in the energy sector.

➵ Gross food consumption

All the food consumed in society (in the sense of disappearance) for the endosomatic metabolism. This quantity includes: 1) final domestic consumption; 2) food used in the operation of the food system itself (animal feed, eggs and seeds used in the hypercycle); and 3) losses and waste in processing, distribution and storage.

➵ Gross food supply (GFS)

Total food supply entering the domestic food supply chain. It can be calculated from the FAO Food Balance Sheets by summing the following categories: local production, imports and changes of stocks.

➵ Gross supply of energy carriers (GSEC)

Corresponds to the supply of energy carriers actually made available to the society by the energy sector and by imports. This supply consists in a mix of energy carriers belonging to the categories of thermal energy (heat and fuels) and mechanical energy (electricity).

➵ Human activity (HA)

The fund element required for controlling the generation and the effective delivery of the applied power generated by exosomatic devices. Human activity (a proxy of the presence of humans in the functional compartment), at the local scale, is measured in hours (per year) and when accounted for within the compartments belonging to the paid work sector is also referred to as human labour.

➵ Hypercyclic compartment

The macro-compartment including the sectors responsible for generating the required flows (food, energy, mineral, water), technology and infrastructures for the whole society. Since the hypercyclic compartment uses part of these flows, technology and infrastructure for its own use, it must generate much more than it consumes (hypercycle) in order to produce an abundant supply of these production factors to the rest of society.

➵ Internal constraints

They are determined by combining information referring to different levels: 1) local-scale metabolic characteristics – the technical coefficients of a given converter to convert an energy input into useful work at a given rate or the rate of evapotranspiration of a given crop per hectare, or the conversion of grain fed to animals into meat; and 2) medium-scale metabolic characteristics determining the congruence between the total amount of production factors and their requirement in each of the functional compartments (the so-called Sudoku effect) of MuSIASEM determined by the organization of data in multi-level tables. Lack of viable operating conditions limits the possibility of expressing functions inside the system and as a consequence limits the possibility of interaction that the metabolic system has with its context. An internal constraint is present when the limits to the expansion of the activity of the system are not determined by shortage of natural resources (supply of inputs or sink capacity for the dumping of wastes) but by the impossibility of taking advantage of them.

➵ Land use (LU)

Hectares of land included in one of the categories used for the accounting of managed land. It represents the social and economic functions and purposes of land.

➵ Managed land (ML)

The part of terrestrial ecosystems that is being used primarily for human activities. Managed land is characterized by the fact that its metabolic characteristics (quantity and quality of standing biomass, density of flows per hectare) are not determined solely by natural processes but are also determined by human management.

➵ Metabolic system

Any system using energy, materials and other natural resources to maintain, reproduce and improve its own existing structures and functions.


The Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism (MuSIASEM) accounting approach was envisioned in the 90s by Mario Giampietro and Kozo Mayumi as an attempt to implement the concept of bio-economics proposed by Georgescu-Roegen. The accounting approach integrates several conceptual tools derived from complexity theory in order to handle the epistemological predicament faced when handling quantitative analyses referring to multiple scales and dimensions. In technical terms this handling requires the ability of integrating information referring to non-equivalent descriptive domains. The Sustainability Sudoku has been developed as a simplified application of the analysis of the metabolic pattern of modern societies using the accounting method MuSIASEM. The MuSIASEM approach is developed by the IASTE research group of the Universitat Autonoma de Barcelona.

➵ Net food supply (NFS)

The quantity of food products and nutrient carriers utilized at the level of the household.

➵ Net supply of energy carriers (NSEC)

The amount of the energy carriers of different types required by the set of functional compartments of the society (including exports) in a given mix.

➵ Power capacity (PC) - (not shown on this website)

The fund element associated with exosomatic devices operating in the functional compartments of society. It is defined as the ability to convert a flow of an energy carrier input into a flow of applied power at the local scale in order to express a defined task (function). Power capacity is measured in kilowatts (kW).

➵ Primary energy source (PES) (relates to ‘primary energy’ in energy statistics)

An energy system capable of taking advantage of physical gradients expressed in biophysical units (not in energy units!) – e.g. tons of coal, cubic metres of gas, tons of uranium, mass and speed of either blowing wind or falling water, intensity of sun radiation, tons of biomass – to make available an amount of ‘energy input’ usable to generate energy carriers. The accounting of primary energy sources is problematic, since they are defined across two logical bifurcations for the accounting: 1) in relation to the nature of energy forms: mechanical versus thermal energy; 2) in relation to the perspective used in the perception: external versus internal view of the metabolic process.

➵ Production factor(s)

The mix of fund elements (human activity, power capacity and land use) and flow elements (energy, water, material) required to guarantee the expression of a given function by a compartment or sub-compartment. The combination of production factors required by a given compartment is described by the data array of ‘end uses’.

➵ Societal metabolism

A notion used to characterize the set of conversions of energy and material flows occurring within a society that are necessary for its continued existence. This set of conversions can be analysed assuming that the society is composed of functional compartments made up of structural elements. The structural elements are the fund elements (people – associated with human activity; exosomatic devices – associated with power capacity; land – associated with land uses and ecological processes), which can be measured using extensive variables (their size). These structural elements are accounted for within functional compartments of the society, expressing specific metabolic characteristics (flow/fund ratios – intensive variables). Then the various flows associated with the functions of the various compartments can be obtained by multiplying the size of the funds by their specific flow/fund ratio: flowi = fundi × (flow/fund)i. The forced relation of congruence of flows across compartments defined at different levels implies that we can expect the emergence of metabolic patterns associated with different structures or functions of a socio-economic system.

➵ Socio-ecological system

The combination of a set of processes of self-organization under human control (determining the viability of the pattern in relation to internal constraints), associated with the concept of society, coupled to a set of natural processes of self-organization beyond human control (determining the stability of boundary conditions for society and therefore the feasibility in relation to external constraints), associated with the concept of ecosystems. In socio-ecological systems societal processes determine the viability of the metabolic pattern and ecological processes determine the feasibility; however, the analysis of these two sets of processes requires the simultaneous adoption of different scales. This means that they cannot be described in a single descriptive domain (and thus they cannot be described in a single quantitative model).

➵ Stock-flow (non-renewable) primary energy sources

Energy systems exploiting favourable physical gradients associated with stocks of material (potential chemical energy in fossil material, and potential nuclear fission energy in uranium).

➵ Strength of the exosomatic hypercycle (SEH)

An indicator of the vigour of the hypercyclic compartment determined by the quality of the natural resources exploited and the quality of the technology and the know-how used in their exploitation. The stronger is the SEH in society, the smaller the share of production factors that must be allocated to the hypercyclic macro-compartment (leaving them for the dissipative compartment). It is formalized as a data array, including the ratios of the total amounts of production factors (fund and flow elements) of the society over the amounts of production factors (fund and flow elements) allocated to the hypercyclic compartment.

➵ Sudoku effect

An integrated set of forced relations of congruence across the characteristics determining the dynamic budgets over data arrays describing end uses included in a multi-level table. The data belonging to the MuSIASEM multi-level tables have to be consistent in relation to vertical constraints, horizontal constraints and block constraints.

➵ Total energy throughput (TET)

In general terms, the total amount of ‘energy’ gathered from the context of the metabolic systems and dissipated inside the metabolic system. Therefore TET can be perceived as a supply/requirement of primary energy sources (external view – ‘energy’ gathered from the context) and/or a supply/requirement of energy carriers (internal view – ‘energy’ dissipated inside). These two perceptions require the adoption of different accounting categories. In relation to the external view TET is measured in energy statistics as either gross energy requirement or total supply of primary energy sources.

➵ Total food throughput (TFT)

The quantity of food products and nutrient carriers disappearing at the level of the whole society for the nutrition of the local population. This quantity is determined by the sum of net food consumption at the household level, the food that is consumed inside the food system for the production of food products (e.g. seeds, feed and eggs) and food losses. This set of assessments refers only to the endosomatic metabolism of the local population. To calculate the total flow of food products in a society one has to add exports to TFT.

➵ Total human activity (THA)

The key fund element of human society, representing the total amount of human time available for conducting different activities. It is measured in hours (h) and calculated as THA = population size × 8,760 hours. HAi represents the human activity allocated to activity or sector i per year: HAi = hours of human activity in sector i per year.

➵ Total managed land (TML)

The fund element representing the total amount of land managed by the society. This amount of TML is divided into different categories of land use, such as agriculture, forestry and urban uses, which can be divided again into subcategories, for example different types of crops within agriculture.

➵ Total power capacity (TPC) - (not shown on this website)

The fund element representing the total amount of power capacity controlled by society. This amount of TPC is divided into different categories, reflecting the allocation of this power capacity to the different metabolic compartments.

➵ Total primary energy supply (energy statistics)

A virtual quantity of energy that is calculated using the physical energy content method to assess the total energy throughput of a society. It estimates a total supply of joules of ‘energy commodities’ to assess the contribution provided by primary energy sources. It is obtained by summing joules of thermal energy (calculated in relation to fossil energy and nuclear energy) to joules of mechanical energy (calculated in relation to hydro and wind energy). However, this sum is not admissible according to what is known in thermodynamics.

➵ Viability

Compatibility with internal constraints. It is one of the conditions for sustainability to be checked with the MuSIASEM approach (together with desirability and feasibility).