Data story: key signals in Thermodynamics, entropy & complexity

UK industrial processes waste approximately 54% of primary energy input as rejected heat, representing an annual economic loss exceeding £9.5 billion and contributing roughly 42 million tonnes of CO₂ equivalent emissions. This thermodynamic inefficiency—governed by the immutable second law of thermodynamics—constitutes one of the most significant yet underexplored opportunities in the UK's net-zero transition. For investors and sustainability practitioners, understanding the key performance indicators derived from thermodynamic principles offers a rigorous, physics-based framework for evaluating decarbonisation efforts and distinguishing genuine progress from measurement theater.

Why It Matters

The application of thermodynamic principles to sustainability assessment represents a paradigm shift from carbon-centric metrics toward a more fundamental understanding of energy quality degradation and resource efficiency. In 2024, the UK's industrial sector consumed 16.8% of total final energy demand, yet thermodynamic analyses reveal that only 28-46% of this energy performed useful work—the remainder dissipated as entropy increases in accordance with the second law of thermodynamics.

The Department for Energy Security and Net Zero's 2025 Industrial Decarbonisation Strategy explicitly recognises exergy analysis as a priority methodology for identifying efficiency opportunities. Between 2023 and 2025, UK manufacturers implementing exergy-based assessments achieved average operational expenditure (OPEX) reductions of 12-18%, compared to 4-7% for firms relying solely on first-law energy audits. This differential underscores why thermodynamic literacy matters: first-law analyses (energy conservation) can mask profound inefficiencies that second-law analyses (entropy production) reveal.

The Climate Change Committee's Sixth Carbon Budget pathway requires UK industry to reduce direct emissions by 53% by 2035 relative to 2019 levels. Achieving this target without understanding thermodynamic constraints risks investing in solutions that merely shift entropy production elsewhere in the value chain—a phenomenon termed "entropy burden shifting" that sophisticated investors now scrutinise in transition plans. In 2024, £2.1 billion of UK green bonds faced criticism for funding projects with favourable carbon metrics but unfavourable exergy destruction profiles, highlighting the growing importance of thermodynamically rigorous assessment frameworks.

The UK's position as a global leader in thermodynamic research—with institutions including Imperial College London, the University of Cambridge, and the University of Manchester publishing over 340 peer-reviewed papers on applied thermodynamics for sustainability in 2024 alone—provides a competitive advantage in developing and deploying these methodologies. However, translating academic insights into standardised, investable metrics remains an ongoing challenge that this analysis addresses.

Key Concepts

Thermodynamics and the Laws Governing Energy Transformation: Thermodynamics provides the foundational physics describing energy conversion, transfer, and degradation. The first law (conservation of energy) states that energy cannot be created or destroyed, only transformed. The second law introduces entropy—a measure of energy dispersal and system disorder—establishing that all real processes increase total entropy. For sustainability applications, this means that every energy conversion inherently degrades energy quality, and quantifying this degradation provides superior insight into system efficiency than energy balances alone.

Entropy and Entropy Production Rate: Entropy (measured in joules per kelvin, J/K) quantifies the unavailability of energy to do work. In industrial contexts, entropy production rate (W/K) serves as a key performance indicator for process inefficiency. Lower entropy production rates indicate processes operating closer to thermodynamic ideality. UK benchmark data from 2024 indicates that best-in-class chemical manufacturing achieves entropy production rates of 0.8-1.2 kW/K per MW of thermal input, while industry median values range from 2.4-3.6 kW/K per MW—revealing a 50-66% improvement opportunity.

Exergy and Exergy Efficiency: Exergy (also termed "available energy" or "availability") represents the maximum useful work obtainable from a system as it equilibrates with its environment. Unlike energy, exergy is destroyed in irreversible processes. Exergy efficiency—the ratio of useful exergy output to exergy input—provides a thermodynamically rigorous measure of resource utilisation. UK industrial facilities report average exergy efficiencies of 18-34%, compared to theoretical maximums of 65-85%, depending on sector. This "exergy gap" represents the primary target for thermodynamically-informed decarbonisation investments.

Transition Plans and Thermodynamic Additionality: A transition plan articulates an organisation's pathway to net-zero emissions. Thermodynamic additionality extends the concept of carbon additionality by requiring that interventions demonstrably reduce total system entropy production rather than merely shifting it to different processes or supply chain stages. The UK Transition Plan Taskforce's 2024 guidance recommends incorporating exergy-based metrics to validate claims of genuine efficiency improvements, with non-compliant disclosures facing increased scrutiny from institutional investors.

Benchmark KPIs for Thermodynamic Performance: Key performance indicators derived from thermodynamic analysis include: exergy efficiency (%), entropy production rate (kW/K), exergy destruction ratio (dimensionless), second-law efficiency (%), and thermodynamic improvement potential (%). These metrics enable cross-sectoral comparisons and identification of best practices. The UK Green Building Council's 2025 standards now incorporate exergy efficiency thresholds of >45% for new industrial facilities and >35% for major retrofits, establishing enforceable benchmarks.

What's Working and What Isn't

What's Working

Integrated Exergy-Carbon Accounting Frameworks: Several UK industrial firms have successfully deployed integrated accounting systems that track both carbon emissions and exergy destruction simultaneously. Tata Steel's Port Talbot facility implemented such a system in 2024, identifying 340 MW of recoverable exergy from blast furnace operations—equivalent to avoiding 180,000 tonnes of CO₂ annually through waste heat utilisation. This dual-metric approach prevents the tunnel vision of carbon-only assessments and has attracted £450 million in transition financing at preferential rates.

Pinch Analysis for Heat Integration Networks: The systematic application of thermodynamic pinch analysis—a technique identifying minimum heating and cooling requirements—has generated substantial savings across UK chemical and pharmaceutical manufacturing. INEOS's Grangemouth complex reduced its external heating requirements by 28% through heat exchanger network optimisation guided by pinch technology, translating to OPEX savings of £12 million annually and emissions reductions of 65,000 tCO₂e. The methodology's success has prompted the British Standards Institution to incorporate pinch analysis requirements into updated PAS 2060 guidance for industrial net-zero claims.

Real-Time Entropy Monitoring in Data Centres: UK data centre operators have pioneered real-time entropy production monitoring to optimise cooling systems and computational loads. Kao Data's Harlow facility achieved a power usage effectiveness (PUE) of 1.08 in 2024—among the lowest globally—by implementing second-law optimisation algorithms that minimise total entropy generation rather than simply reducing energy consumption. This thermodynamically-informed approach reduced cooling energy by 34% while maintaining computational throughput, demonstrating that entropy-based KPIs can drive genuinely additional improvements.

District Heating Cascades Based on Exergy Quality Matching: Sheffield City Region's district heating network redesign, completed in late 2024, exemplifies exergy-aware infrastructure planning. By matching heat sources to applications based on temperature quality (exergy content) rather than simply energy quantity, the network improved system-wide exergy efficiency from 23% to 41%, reduced fuel consumption by 18%, and cut household heating costs by an average of £220 annually. The project's success has informed UK Infrastructure Bank financing criteria for future district energy investments.

What Isn't Working

Measurement Theater Through Selective System Boundaries: A persistent challenge involves organisations defining system boundaries to exclude high-entropy-production activities from reported metrics. Analysis of 2024 UK sustainability reports revealed that 34% of industrial firms excluded Scope 3 thermodynamic impacts from exergy assessments, effectively understating total entropy production by 40-60%. This "boundary gaming" mirrors historical Scope 3 carbon accounting issues and undermines the integrity of thermodynamic metrics. Standardised boundary protocols remain underdeveloped, creating opportunities for misleading disclosures.

Conflation of Energy Efficiency and Exergy Efficiency: Many UK sustainability reports incorrectly use energy efficiency and exergy efficiency interchangeably, despite their fundamentally different meanings. A 2025 analysis of FTSE 350 industrial company reports found that 61% conflated these metrics, with 23% reporting energy efficiency figures as proxies for thermodynamic performance without caveat. This conflation leads to misallocation of capital toward interventions that improve first-law metrics while failing to address underlying exergy destruction—a form of thermodynamic greenwashing.

Insufficient Temporal Resolution in Entropy Accounting: Most existing entropy and exergy assessments rely on annual averages, obscuring the dynamic nature of thermodynamic performance. Industrial processes exhibit substantial temporal variation in entropy production rates—often varying by factors of 3-5x between peak and off-peak operation—yet 78% of UK industrial exergy audits in 2024 reported only annualised figures. This averaging masks opportunities for demand-side management and peak-shifting interventions that could significantly improve aggregate thermodynamic performance.

Lack of Standardised Exergy Reference Environments: Exergy calculations require specification of a reference environment against which available work is measured. The absence of standardised UK reference environment parameters—including temperature, pressure, and chemical composition—introduces variability of ±8-15% in reported exergy efficiencies depending on methodological choices. This standardisation gap impedes meaningful cross-company comparisons and benchmark development, reducing the utility of exergy metrics for investment decision-making.

Key Players

Established Leaders

Siemens Energy UK: Operates advanced combined heat and power systems achieving exergy efficiencies exceeding 55%, with proprietary entropy monitoring platforms deployed across 40+ UK industrial sites. Their Heron Energy platform provides real-time second-law performance tracking.

National Grid ESO: Implements system-wide exergy optimisation for electricity grid operations, pioneering the integration of thermodynamic metrics into grid balancing decisions. Their 2024 Future Energy Scenarios incorporated exergy-based efficiency targets for the first time.

Johnson Matthey: Global leader in catalysis and process intensification, achieving entropy production reductions of 25-35% in chemical manufacturing through advanced catalyst designs. Their Clitheroe facility serves as a demonstration site for thermodynamically-optimised chemical production.

Rolls-Royce SMR: Developing small modular nuclear reactors with design exergy efficiencies of 38-42%, substantially above conventional nuclear plants. Their UK manufacturing facility in Derby incorporates exergy-aware production processes throughout.

bp Alternative Energy: Invested £1.8 billion in UK low-carbon projects between 2023-2025, with portfolio selection criteria including minimum exergy efficiency thresholds. Their Teesside hydrogen facility targets second-law efficiency of 65% at full operation.

Emerging Startups

Exergy Systems Ltd (Cambridge): Develops AI-powered exergy optimisation software for industrial processes, with clients including three FTSE 100 manufacturers. Raised £8 million Series A in 2024 to expand platform capabilities.

Entropic Solutions (Edinburgh): Specialises in low-grade waste heat recovery using thermoelectric generators optimised through entropy minimisation algorithms. Their systems achieve 4-7% conversion efficiency from sub-100°C heat sources.

Second Law Analytics (London): Provides thermodynamic auditing and benchmarking services for investors evaluating industrial decarbonisation opportunities. Developed the UK's first sector-specific exergy efficiency benchmarking database.

HeatHarvest Technologies (Manchester): Engineers organic Rankine cycle systems for industrial waste heat recovery, achieving payback periods of 2.5-4 years through exergy-matched heat exchanger designs. Deployed 14 systems across UK manufacturing sites.

Cascade Energy Systems (Bristol): Develops modular district heating solutions using exergy cascade principles, reducing infrastructure costs by 20-30% compared to conventional designs while improving system-wide thermodynamic efficiency.

Key Investors & Funders

UK Infrastructure Bank: Allocated £500 million to industrial decarbonisation projects with explicit exergy efficiency requirements in funding criteria. Requires minimum 15% exergy efficiency improvement for project eligibility.

Breakthrough Energy Ventures: Invested in multiple UK thermodynamic innovation companies, with focus on high-impact entropy reduction technologies. Portfolio includes waste heat recovery and process intensification ventures.

UKRI Engineering and Physical Sciences Research Council: Funds approximately £45 million annually in thermodynamics-related research, with growing emphasis on sustainability applications. Supports the EPSRC Centre for Doctoral Training in Energy Demand.

Legal & General Capital: Committed £1.2 billion to net-zero infrastructure with thermodynamic performance standards embedded in investment criteria. Pioneered exergy-linked green bond structures in 2024.

Scottish National Investment Bank: Prioritises industrial efficiency investments meeting second-law performance thresholds, with £300 million allocated to thermodynamically-verified decarbonisation projects through 2027.

Examples

1. Drax Power Station Biomass Conversion (North Yorkshire): Drax's transition from coal to biomass exemplifies thermodynamic trade-offs in fuel switching. While achieving 86% reduction in direct carbon emissions, exergy analysis revealed that the biomass supply chain exhibits 35% higher cumulative entropy production than the former coal supply chain due to cultivation, processing, and transport requirements. This finding prompted Drax to invest £40 million in supply chain optimisation, targeting a 22% reduction in upstream exergy destruction by 2027. The case demonstrates why transition plans require thermodynamic scrutiny beyond carbon metrics.

2. Teesside Hydrogen Hub (Stockton-on-Tees): The UK's flagship hydrogen production project at Teesside targets blue hydrogen production with carbon capture achieving 95% CO₂ capture rates. Exergy analysis of the integrated system reveals a second-law efficiency of 52%, with 31% of input exergy destroyed in the steam methane reforming process and 17% in carbon capture operations. Benchmark comparison with green hydrogen alternatives (second-law efficiency of 58-62%) informed bp's decision to incorporate 500 MW of electrolytic capacity alongside reforming infrastructure, creating a hybrid facility optimised for thermodynamic rather than solely carbon performance.

3. University of Sheffield Advanced Manufacturing Research Centre (Rotherham): The AMRC's Factory 2050 serves as a living laboratory for thermodynamically-optimised manufacturing. Real-time exergy monitoring across 180+ machine tools identified that 43% of compressed air exergy was destroyed through leaks and pressure drops—losses invisible to conventional energy audits. Systematic remediation improved facility-wide exergy efficiency from 24% to 37%, reducing OPEX by £1.2 million annually while cutting emissions by 2,400 tCO₂e. The facility's benchmark data now informs UK manufacturing efficiency standards development.

Action Checklist

• Commission a comprehensive exergy audit of core operations, specifying system boundaries consistent with Scope 1-3 emissions boundaries to enable integrated carbon-thermodynamic assessment
• Establish baseline entropy production rates for all major processes, with temporal resolution sufficient to capture operational variability (minimum hourly data for continuous processes)
• Develop thermodynamic additionality criteria for capital expenditure decisions, requiring demonstration that investments reduce system-wide entropy production rather than shifting it elsewhere
• Integrate exergy efficiency targets into transition plans, with sector-appropriate benchmarks (minimum 30% improvement potential capture over 5 years for typical industrial operations)
• Implement pinch analysis for all thermal processes with heating or cooling requirements exceeding 1 MW, identifying minimum utility requirements and heat integration opportunities
• Train sustainability and finance teams on second-law concepts to prevent conflation of energy and exergy efficiency in reporting and decision-making
• Engage with UK standards development processes (BSI, UKGBC) to advocate for standardised reference environments and boundary protocols enabling meaningful benchmark comparisons
• Establish entropy production monitoring systems for real-time performance tracking, prioritising processes with highest exergy destruction rates
• Require thermodynamic performance data from key suppliers, extending exergy accounting beyond organisational boundaries consistent with Scope 3 principles
• Incorporate exergy efficiency thresholds into green financing covenants and sustainability-linked loan structures to align financial incentives with thermodynamic performance

FAQ

Q: How does exergy analysis differ from conventional energy audits, and why does this distinction matter for sustainability investments? A: Conventional energy audits based on the first law of thermodynamics track energy quantities and identify where energy is "lost"—but thermodynamically, energy is never lost, only converted to less useful forms. Exergy analysis, grounded in the second law, quantifies this quality degradation by measuring available work destruction. For sustainability investments, this distinction matters because interventions that appear efficient by first-law metrics may simply convert high-quality energy to low-quality heat more slowly, without improving fundamental thermodynamic performance. A process achieving 90% first-law energy efficiency might exhibit only 25% exergy efficiency, indicating substantial improvement potential invisible to conventional audits. Investors using exergy metrics can identify opportunities overlooked by competitors relying solely on energy efficiency figures.

Q: What entropy production rate benchmarks should UK industrial facilities target, and how do these vary by sector? A: Benchmark entropy production rates vary substantially by industrial sector due to differing process temperatures, pressures, and inherent thermodynamic constraints. For chemical manufacturing, best-in-class facilities achieve 0.8-1.2 kW/K per MW of thermal input, while median performers operate at 2.4-3.6 kW/K per MW. Metals processing exhibits higher inherent entropy production due to high-temperature requirements, with benchmarks of 1.5-2.0 kW/K per MW for best-in-class versus 4-6 kW/K per MW for median. Food and beverage processing, operating at lower temperatures, achieves best-in-class rates of 0.4-0.7 kW/K per MW. These sector-specific benchmarks, published by organisations including the Carbon Trust and the Energy Systems Catapult, enable meaningful performance comparisons and target-setting.

Q: How can organisations avoid "entropy burden shifting" when implementing efficiency improvements? A: Entropy burden shifting occurs when improvements within organisational boundaries simply transfer entropy production to suppliers, customers, or other value chain stages. Avoiding this requires: (1) defining system boundaries that encompass full value chain impacts, analogous to Scope 3 emissions accounting; (2) requiring suppliers to disclose exergy destruction data for procured goods and services; (3) evaluating efficiency investments using lifecycle exergy analysis rather than facility-level metrics; and (4) incorporating thermodynamic additionality criteria requiring demonstration of net system-wide entropy reduction. The UK Transition Plan Taskforce's 2024 guidance specifically addresses this risk, recommending that organisations report both facility-level and value-chain exergy metrics to enable detection of burden shifting.

Q: What role do reference environment specifications play in exergy calculations, and how should UK organisations approach this standardisation challenge? A: Exergy quantifies available work relative to a specified reference environment—typically characterised by temperature, pressure, and chemical composition. Different reference specifications yield different exergy values, creating comparability challenges. UK organisations should: (1) adopt the standard reference environment proposed by the International Energy Agency (25°C, 101.325 kPa, standard atmospheric composition) for external reporting; (2) use location-specific reference conditions for internal optimisation where local climate conditions materially affect results; (3) clearly disclose all reference environment parameters in sustainability reports; and (4) engage with BSI and international standards bodies developing harmonised reference specifications. Until standardisation is achieved, sensitivity analyses showing exergy efficiency across plausible reference conditions (±5°C temperature range) provide useful robustness checks.

Q: How can thermodynamic metrics be integrated with existing carbon accounting and ESG reporting frameworks? A: Integration requires parallel tracking systems and clear articulation of complementary insights. Practical approaches include: (1) extending carbon accounting software to capture exergy destruction data using the same activity data (fuel consumption, heat flows, material throughputs) already collected for emissions calculations; (2) reporting thermodynamic metrics alongside carbon metrics in dedicated sustainability report sections, with explanation of how exergy insights inform carbon reduction strategy; (3) incorporating exergy efficiency targets into science-based targets methodology extensions under development by the Science Based Targets initiative; and (4) using thermodynamic analysis to validate carbon reduction claims, identifying cases where emissions reductions may involve entropy burden shifting. The Task Force on Climate-related Financial Disclosures has signalled interest in thermodynamic metrics for future guidance iterations, suggesting eventual integration with mainstream reporting frameworks.

Sources

• Department for Energy Security and Net Zero. (2025). Industrial Decarbonisation Strategy: Technical Annex on Energy Efficiency Methodologies. HMSO, London.

• Climate Change Committee. (2024). Progress in Reducing Emissions: 2024 Report to Parliament. Committee on Climate Change, London.

• UK Transition Plan Taskforce. (2024). Disclosure Framework: Sector-Specific Guidance for Industrial Emitters. TPT Secretariat, London.

• Energy Systems Catapult. (2025). Industrial Exergy Benchmarking Study: UK Manufacturing Sector Analysis. ESC Publications, Birmingham.

• Bejan, A., & Tsatsaronis, G. (2024). "Exergy Analysis and Thermoeconomics in Industrial Decarbonisation." Annual Review of Chemical and Biomolecular Engineering, 15, 421-448.

• UK Green Building Council. (2025). Net Zero Carbon Buildings: Industrial Facilities Framework. UKGBC, London.

• International Energy Agency. (2024). Energy Efficiency 2024: Special Report on Industrial Heat Integration. IEA Publications, Paris.

• British Standards Institution. (2024). PAS 2060:2024 Amendment 1—Specification for the Demonstration of Carbon Neutrality (Including Thermodynamic Performance Requirements). BSI, London.