Exergy and the Circular Economy

The Failure of Mass-Based Metrics

The circular economy has successfully established a new vocabulary for business and policy, yet it continues to operate without a physically rigorous meter. Current statistics rely almost exclusively on mass ratios—measuring tonnes recycled or the percentage of material input cycled back into the economy. By these flawed metrics, global circularity is currently estimated at approximately seven percent and falling. However, these figures are misleading because mass is fundamentally blind to quality. In a mass-based ledger, a tonne of construction sand and a tonne of refined neodymium are treated as identical units of value, despite the vast difference in the thermodynamic investment required to produce them.

This blindness to quality leads to significant distortions in national and corporate reporting. For instance, a smelter that recovers bulk copper while vaporizing rare elements like gallium and indium can still post an excellent mass recovery rate. More concerning is the treatment of incineration, which is frequently booked as "recovery" in national statistics. While this process salvages a material’s chemical exergy as one-shot heat, it destroys all higher-order material value and configurational order, yet it is often credited as a circular act. The current metrics do not merely lack precision; they frequently invert value rankings exactly where rigorous ranking is most required.

Exergy as the Superior Meter

To accurately measure the true value of materials, the circular economy must adopt the same second-law currency applied to energy systems: exergy. In the context of matter, exergy is defined as the thermodynamic value of a material, representing the minimum work required to reconstitute it from the dispersed, "dead" state of the reference environment. It represents what nature and industry have invested against entropy to create a specific material and give it function.

By using exergy as a meter, the circular economy can finally adjudicate between different material strategies based on the fraction of invested work each loop returns to service. This approach recognizes that the value worth preserving is not mass—which is indestructible—but order. The chemical exergy of a substance accounts for the work standing in its composition, while concentration exergy accounts for the effort required to gather it from dilution. Transitioning to exergy-based metrics allows for a "circular exergy fraction" that reweights circularity rates by actual value, ensuring that claims of sustainability are grounded in engineering rather than theatre.

Matter as Frozen Work: The Exergy Scale

Every refined material is a thermodynamic achievement: atoms gathered from dispersal, separated from their neighbors, reduced from their oxides, and arranged into function. A material's exergy is its thermodynamic value, representing what nature and industry invested against entropy to make it what it is. In this framework, matter is viewed as frozen work, layered by the chemical and concentration exergy required for its existence. Quantifying these values reveals that the material economy spans three orders of magnitude in thermodynamic altitude, a reality that mass-based metrics fail to capture.

Chemical and Concentration Exergy

Chemical exergy represents the maximum work obtainable—or the minimum work required—to bring a substance into complete equilibrium with the reference environment. The values of common industrial materials provide a map of these investments:

Beyond chemical composition, concentration exergy prices the "gathering" of materials. Thermodynamics dictates that the minimum work to concentrate a substance rises as the logarithm of the concentration ratio. In practice, this manifests as a gradient tax on depletion: halving an ore grade roughly doubles the extraction energy required per tonne of metal. As industry mines down the grade curve, the exergy cost per tonne climbs, making the preservation of high-grade materials a physical necessity.

Thanatia and the Two Deaths of Matter

To measure the true price of dispersal, the concepts of Thanatia and exergy replacement cost provide a physics-derived criticality ranking. Thanatia represents a hypothetically exhausted Earth where all minerals are dispersed to crustal background levels. The exergy replacement cost is the work needed to reconstitute a material from this dead state, often reaching tens to hundreds of times the material's chemical exergy. This ranking puts rare earths, gallium, and indium at the summit of thermodynamic rarity, reflecting their usable existence as a significant investment of work.

A material suffers two distinct thermodynamic deaths during its lifecycle:

• Chemical death: Occurs through oxidation, combustion, or degradation, where the standing chemical exergy is spent.
• Configurational death: Occurs through mixing, contamination, or dispersal. The substance survives, but its concentration and purity are destroyed.

"Waste is the name an economy gives to value it has stopped measuring—and circularity should be measured as exergy retained, the fraction of invested work each loop returns to service."

Configurational death is the circular economy's silent enemy. While it is invisible to mass statistics, it destroys the grade that separation processes paid for, making recovery as exergy-intensive as primary production.

The R-Hierarchy Derived from Physics

The circular economy’s fundamental ladder of strategies—reduce, reuse, repair, remanufacture, recycle, and recover—is traditionally justified through intuition or policy convention. However, within a thermodynamic framework, this hierarchy is not merely a preference but a physical derivation. By ranking each strategy according to the fraction of embodied exergy investment it returns to service, the ladder assembles itself according to the second law of thermodynamics.

The Physics of Preservation

At the summit of the hierarchy, reduce and reuse represent the most efficient strategies because they preserve over 90 percent of the "full stack" of embodied exergy. Reduction preserves everything by spending nothing, while reuse maintains the chemical, concentration, and configurational exergy, plus the manufacturing work standing in the finished form, at the minimal cost of logistics and cleaning. Remanufacturing follows closely, typically retaining 60–90 percent of the original work invested in a product by keeping the material and the majority of the forming work, requiring fresh exergy only for replaced or worn components.

The Separation Debt and Recycling

Recycling occupies a lower rung because the product’s configuration is destroyed, even if the material substance is saved. Its value is determined by the "separation debt": the massive exergy investment required for primary gathering and reduction that, once paid, does not need to be spent again. The exergy dividend of recycling is significant for metals:

However, the audit distinguishes between closed-loop recycling and downcycling. While closed-loop processes preserve both substance and specification, downcycling saves the substance but loses the grade. This results in significant exergy forfeiture, as the concentration exergy needed to undo contamination (such as copper-contaminated steel or mixed polymers) is rarely reinvested, leading to a permanent loss of material quality.

Adjudicating the Ladder

This derivation adjudicates hard cases that mass-based metrics cannot resolve. It explains why the hierarchy may legitimately invert—such as when the reuse of an inefficient, exergy-hungry boiler destroys more exergy in operation than was embodied in its manufacture. Furthermore, it exposes "recovery" euphemisms; incinerating plastic for energy recovery salvages only the chemical exergy at the price of all higher-order order, returning perhaps a tenth of the material's standing value. By measuring exergy retained, the R-hierarchy moves from environmental theatre to rigorous engineering.

Waste as a Portfolio of Misplaced Assets

When the material economy is graded by standing exergy rather than bulk weight, the concept of "waste" dissolves into a spectrum of misplaced assets. This categorization reveals that many discarded streams are thermodynamically richer than the primary ores industry currently extracts. By mapping these discards according to their standing chemical exergy, concentration exergy, and the work required to recover them, the circular economy can prioritize its efforts based on real thermodynamic value rather than mass-ledgers that treat all tonnes as equal.

The Spectrum of Discards

At the summit of the waste spectrum lies electronic waste. Circuit boards and high-tech components represent an extraordinary concentration of thermodynamic order, often out-grading gold ore by an order of magnitude. These streams carry the thermodynamically rarest elements in the industrial inventory, yet formal recovery efforts currently reach barely a fifth of the total stream. Similarly, the burgeoning fleet of electric vehicles (EVs) represents a "scheduled ore body" accumulating on the world's roads. The harvest calendar for this asset is not determined by geological discovery, but by vehicle age curves; the terawatt-hours of battery capacity sold today define the black-mass supply available for recovery in the next decade.

Hidden Assets in the Margins

Even at the lower end of the spectrum, high-value assets are frequently ignored by traditional accounting. Tailings, slags, and ashes are often considered "spent" by mass-based standards, yet they frequently serve as the residence for critical by-product metals such as germanium, gallium, and cobalt. These speciality metals are often passengers in bulk-metal flowsheets, and their loss represents a failure to account for thermodynamic rarity. A smelter that vaporizes gallium while focusing only on mass recovery of copper is, in exergy terms, destroying a replacement value far higher than the primary invoice it manages to salvage.

The Advantage of Urban Mining

Urban mining—the recovery of materials from buildings, vehicles, and devices—offers a profound thermodynamic advantage over primary extraction. In these anthropogenic stocks, the concentration work has already been performed and is currently "standing" in the material. The central challenge of the circular economy is avoiding the "second death"—configurational death—during collection and processing. While mass is never lost, the purity and order of these materials are easily destroyed through mixing, contamination, or shredding. Preventing this second death ensures that the exergy invested in the material’s original gathering and refining remains accessible, rather than being forfeited to the entropy of a landfill or a low-grade downcycling loop.

The Transition Loops: Batteries and Carbon

The technical audit of material flows in the current energy transition reveals that circularity is not merely a matter of mass, but a battle for the retention of exergy. Among the most critical material flows, the battery loop serves as the industry’s pilot plant. Every electric vehicle banks roughly half a tonne of high-exergy material, including lithium, nickel, cobalt, and graphite. These elements are refined to battery grade at concentration costs that dominate the pack’s embodied exergy account. The accumulation of these materials represents a scheduled ore body whose harvest is dictated by the vehicle age curve, presenting an urban mining opportunity far richer than primary ores.

The EU Battery Regulation serves as the foundational technical template for this transition, as it is the first law written "at grade." Moving beyond simple mass ratios, it mandates per-element recovery rates for lithium, cobalt, nickel, and copper at specified purities. By requiring digital passports that carry composition, provenance, and state-of-health data, the regulation establishes a physically rigorous assay sheet for the materials economy. This ensures that circularity is measured by the fraction of invested work returned to service rather than the mere weight of material collected.

The mechanisms of recovery determine the exergy dividend. For batteries, hydrometallurgical recovery—utilizing aqueous routes of leaching, purification, and precipitation—is the preferred technical path. Unlike pyrometallurgical routes that often forfeit lithium to slag and consume fuel exergy, the hydrometallurgical process allows for the return of high-purity lithium and nickel to the cathode supply chain using electricity as the primary input. This "closed-loop" recycling pays the thermodynamic separation debt only once, preserving the high standing exergy of refined metals.

Carbon and polymers present a different set of thermodynamic constraints. The audit of carbon loops clarifies that mechanical recycling of plastics is technically superior to chemical recycling because it keeps polymer chains intact, preserving nearly all the standing chemical exergy (roughly 30–47 MJ/kg). Chemical recycling—such as pyrolysis or depolymerization—is a necessary but thermodynamically expensive fallback for contaminated or multilayer streams, as it spends process exergy to return polymers to a monomer state. Similarly, Carbon Capture and Use (CCU) is recognized as a thermodynamically expensive strategy because CO₂ exists in a "dead state." CCU must pay the full reduction exergy to re-energize the carbon, and technical priority should therefore be given to long-lived materials like polymers or aggregates that fix carbon, rather than fuels that repeat the combustion-exhaust cycle.

These critical loops demonstrate the core theorem of second-law economics: the higher the state of order preserved, the less the economy pays to keep it. Whether in batteries or carbon, the objective is to prevent "configurational death"—the mixing and contamination that destroys the work nature and industry previously invested.

Implementing the Exergy Meter

The circular economy currently lacks a rigorous instrument to measure the thermodynamic value it claims to preserve. While existing statistics rely on mass ratios—counting tonnes of material recycled or diverted from landfill—these figures are fundamentally blind to quality. A tonne of sand and a tonne of neodymium are recorded as identical quantities, despite their vastly different industrial and thermodynamic utility. To move from theatre to engineering, firms and regulators must adopt a meter based on exergy: a measure of the work required to reconstitute a material from its dispersed environmental state.

New Indicators for Firms and Regulators

Practical implementation requires a set of computable indicators that replace "tonnage theatre" with a physically grounded ledger. Four primary metrics are proposed for institutional adoption:

• Exergy Retention Ratio (ERR): This loop-level indicator measures the standing exergy returned to service at grade compared to the standing exergy entering the end-of-life stage. It distinguishes high-value closed-loop recycling from downcycling, which saves substance but loses specification.
• Circular Exergy Fraction (CEF): At the firm or national level, this reweights corporate circularity rates by thermodynamic value rather than tonnes. Under this metric, the recovery of specialty metals stops vanishing into the statistical noise of bulk minerals like sand.
• Exergy Replacement Cost Avoided: Based on the concept of "Thanatia" (a hypothetically exhausted Earth), this prices the dispersal debt each loop prevents, reflecting the true cost of losing rare elements to the crustal background.
• Cumulative Exergy Demand: A system-level measure that tracks the total work potential drawn from nature to deliver a service, uniting circular economy audits with energy efficiency ledgers.

Data Layers and Audit Requirements

The transition to these indicators depends on a robust information layer. Digital product passports are essential to supply the composition, provenance, and state-of-health data required for exergy audits. By providing an assay sheet for the "urban mine," these passports allow recyclers to identify and defend the grade of materials before they are processed. Furthermore, policy must shift toward mandating recovery at specified purities, similar to the template established by Europe’s Battery Regulation, which specifies per-element recovery rates for lithium, nickel, and cobalt.

Economics of Preservation

Implementing the exergy meter also clarifies the economic priority of design. Design for disassembly is identified as the cheapest concentration process available to industry, as order preserved by intention costs nothing to recover at end-of-life. Conversely, the "second death" of a material—configurational death through mixing and contamination—imposes a heavy thermodynamic tax because undoing such disorder often costs more than primary production. By adopting exergy-based reporting, firms can finally align their circularity strategies with the second law of thermodynamics, ensuring that the work invested in materials is not spent twice.

Key findings

• The Aristocracy of Metals — Bulk metals like aluminium and steel show high recycling dividends because their initial reduction/concentration exergy is banked; remelting aluminium saves 95% of primary energy.
• Thermodynamic Rarity Gap — Speciality metals like gallium and tellurium have the highest exergy replacement costs but recycling rates below 1% due to configurational dispersal at the design stage.
• Two Deaths of Matter — Configurational death (mixing and contamination) is the silent enemy of circularity, destroying value even when no mass is lost.
• Hierarchy Inversion — Mass-based statistics can invert value rankings, such as crediting plastic incineration as 'recovery' despite it salvaging only a tenth of the material's standing value.

Method and assumptions

The paper utilizes second-law thermodynamics to establish a material valuation framework. It relies on Szargut's standard chemical exergy tables and Valero's 'Thanatia' model for exergy replacement costs. The analysis applies these physical constants to global material flow accounts (from the Circularity Gap and UNEP reports) and industrial data on recycling efficiencies. The framework assumes a reference environment of atmospheric gases, seawater, and crustal minerals to calculate chemical equilibrium. System boundaries include the full lifecycle (Cradle-to-Gate and End-of-Life), comparing cumulative exergy demand (CExD) with standing exergy to determine retention ratios.

Where it applies

• Corporate Sustainability Reporting — Firms can publish a 'Material Exergy Account' to show the true fraction of value returned to service, moving beyond tonnage-based claims.
• Product Design Specification — Engineers can use exergy retention ratios to adjudicate between materials, prioritising mono-materials and mechanical fasteners that prevent configurational death.
• Regulatory Compliance — Policy makers can apply the 'Battery Regulation' template to electronics and textiles, setting recovery targets by element and purity (at grade).

Terms used

• Chemical Exergy — The maximum work obtainable when bringing a substance into complete equilibrium with the standard reference environment.
• Concentration Exergy — The minimum work required to gather a substance from a dilute state to a desired purity.
• Configurational Death — The loss of material value through mixing, contamination, or dispersal, even when the substance itself is not chemically destroyed.
• Exergy Retention Ratio — The fraction of a material's standing exergy that is returned to service at the same grade or specification.
• Thanatia — A hypothetical state of an exhausted Earth where all concentrated mineral deposits have been dispersed into the crustal background.
• Black Mass — The crushed and shredded remains of batteries from which valuable metals like lithium and nickel are extracted.

Questions and answers

Why is exergy better than mass for measuring circularity?

Mass counts quantity but is blind to quality. Exergy measures the 'frozen work' or order within a material, allowing us to distinguish high-value speciality metals from low-value minerals and recognize the value lost when materials are contaminated or downcycled.

Is recycling always the best option according to the exergy ledger?

No. The second law derives the R-hierarchy where 'reduce' and 'reuse' are superior because they preserve the full stack of embodied exergy. Recycling is an 'aristocratic' strategy for metals where the separation debt is high, but it ranks below remanufacturing.

What is 'downcycling' in thermodynamic terms?

Downcycling occurs when the substance is retained but its grade or specification is lost, such as copper-contaminated steel. It preserves chemical exergy but destroys configurational exergy, often requiring primary material to be added elsewhere to meet high-grade demands.

How can designers prevent the 'second death' of materials?

Designers can prevent configurational death by using mono-materials, mechanical fasteners instead of adhesives, and clearly marking polymers, which keeps separation costs low and maintains material purity at end-of-life.

How to cite

Bakker, W. A. (2026). Exergy and the Circular Economy: Measuring the True Value of Materials, Energy and Waste. Exerginity White Paper Series, No. 4. August 2026. Exerginity.