Thermodynamics, entropy & complexity KPIs by sector (with ranges)

Every industrial process, every energy conversion, and every material transformation is governed by the laws of thermodynamics. Yet most sustainability reporting treats energy as a simple input-output accounting exercise, ignoring the thermodynamic quality of energy flows and the entropic costs embedded in production systems. This oversight matters because the second law of thermodynamics places hard physical limits on efficiency improvements, and organisations that measure thermodynamic performance correctly can identify the 20 to 40% of energy losses that conventional metrics miss entirely. This article maps the essential thermodynamic, entropy, and complexity KPIs across sectors, providing benchmark ranges drawn from UK and international industrial data, and separating the metrics that drive genuine insight from those that obscure it.

Why It Matters

The UK's Climate Change Committee estimates that industrial processes account for approximately 16% of the nation's territorial greenhouse gas emissions, with energy-intensive industries including chemicals, steel, cement, glass, and food processing consuming over 280 TWh of primary energy annually. The UK government's Industrial Decarbonisation Strategy, updated in 2025, sets a target of reducing industrial emissions by 67% by 2035 relative to 2018 levels. Achieving this target requires more than fuel switching; it demands a fundamental improvement in how efficiently energy is converted, distributed, and consumed within industrial systems.

Thermodynamic analysis reveals why. Conventional energy efficiency metrics, typically expressed as useful energy output divided by total energy input, capture first-law efficiency but miss second-law (exergetic) losses. A steam boiler operating at 92% first-law efficiency may have an exergetic efficiency of only 35 to 45%, meaning that more than half the thermodynamic work potential of the fuel is irreversibly destroyed through entropy generation. The UK Energy Research Centre found that applying exergy analysis to the entire UK industrial sector reveals approximately 120 TWh of annual thermodynamic waste that is invisible to standard energy audits, equivalent to roughly 18% of total industrial primary energy consumption.

Complexity science adds another dimension. Modern industrial systems are networks of coupled processes where local optimisation frequently degrades system-level performance. A chemical plant may optimise individual unit operations to 90%+ efficiency while the overall plant operates at 55 to 65% thermodynamic efficiency due to thermal cascading mismatches, unnecessary mixing losses, and suboptimal heat integration. Understanding and measuring system complexity is essential for identifying where intervention will yield genuine improvements versus where it will simply shift losses from one process to another.

For UK sustainability professionals navigating the Streamlined Energy and Carbon Reporting (SECR) requirements, the Task Force on Climate-related Financial Disclosures (TCFD) recommendations, and emerging International Sustainability Standards Board (ISSB) frameworks, thermodynamic KPIs provide a rigour that carbon-only metrics lack. Organisations that measure exergetic performance can identify stranded efficiency potential, prioritise capital allocation, and set reduction targets grounded in physical limits rather than arbitrary percentages.

Key Concepts

Exergy quantifies the maximum useful work obtainable from a system as it reaches equilibrium with its environment. Unlike energy, which is always conserved (first law), exergy is destroyed in every real process through irreversibilities such as heat transfer across finite temperature differences, fluid friction, mixing, and chemical reactions proceeding away from equilibrium. Exergy destruction is directly proportional to entropy generation and represents a permanent loss of work potential. Measuring exergy efficiency reveals where thermodynamic value is being destroyed, not merely transferred.

Entropy Generation Rate measures the rate at which irreversible processes within a system produce entropy. According to the Gouy-Stodola theorem, the rate of exergy destruction equals the product of the ambient temperature and the entropy generation rate. Tracking entropy generation by process unit allows engineers to pinpoint the specific operations, heat exchangers, reactors, compressors, or mixing stages, where the largest thermodynamic losses occur. This metric transforms thermodynamic analysis from a theoretical exercise into an operational diagnostic tool.

Pinch Analysis is an established methodology for optimising heat recovery in industrial processes by identifying the thermodynamic pinch point, the temperature level at which the minimum temperature difference between hot and cold process streams occurs. The technique was developed at the University of Manchester (then UMIST) and remains the foundation for industrial heat integration. Pinch analysis typically reveals that 20 to 40% of external heating and cooling requirements can be eliminated through improved heat exchanger networks.

Network Complexity Index quantifies the degree of coupling and interdependence among process units within an industrial system. Higher complexity does not inherently indicate inefficiency, but it does indicate that local changes propagate unpredictably through the system. Measuring complexity helps sustainability teams understand why some efficiency interventions produce expected results while others generate unintended consequences that partially or fully offset the intended improvement.

Thermodynamic KPIs by Sector

Power Generation

KPI	Below Average	Average	Above Average	Top Quartile
Exergetic Efficiency (CCGT)	<52%	52-57%	57-62%	>62%
Exergetic Efficiency (Coal)	<30%	30-36%	36-40%	>40%
Entropy Generation Rate (kW/K per MW output)	>2.8	2.0-2.8	1.4-2.0	<1.4
Heat Rate Deviation from Design (%)	>8%	5-8%	2-5%	<2%
Condenser Exergy Destruction (% of fuel exergy)	>18%	14-18%	10-14%	<10%
Auxiliary Power Consumption (% gross output)	>7%	5-7%	3-5%	<3%

UK combined cycle gas turbine plants operating at top-quartile exergetic efficiency (above 62%) include Drax's Selby gas plant and SSE's Keadby 2, both achieving these levels through advanced turbine inlet cooling and optimised heat recovery steam generator configurations. The median UK CCGT fleet operates at approximately 55% exergetic efficiency, indicating substantial thermodynamic improvement potential even within the existing gas generation fleet. The gap between first-law thermal efficiency (typically reported at 58 to 63%) and exergetic efficiency (52 to 62%) reflects the irreversibilities in combustion, heat transfer, and steam expansion that first-law reporting conceals.

Chemicals and Petrochemicals

KPI	Below Average	Average	Above Average	Top Quartile
Overall Plant Exergetic Efficiency	<25%	25-35%	35-45%	>45%
Column Second-Law Efficiency	<8%	8-15%	15-22%	>22%
Heat Integration Achievement (% of pinch target)	<55%	55-70%	70-85%	>85%
Reactor Entropy Generation (kJ/K per tonne product)	>850	550-850	350-550	<350
Utility System Exergy Losses (% total site exergy input)	>30%	22-30%	15-22%	<15%
Network Complexity Index	>0.85	0.65-0.85	0.45-0.65	<0.45

Distillation columns are consistently the largest single source of exergy destruction in chemical plants, typically consuming 40 to 60% of total plant utility exergy while operating at second-law efficiencies of only 5 to 15%. INEOS's Grangemouth complex undertook a comprehensive exergy audit in 2023, identifying that 38% of site-wide exergy destruction occurred in its distillation train. Targeted interventions, including dividing wall column retrofits and heat pump-assisted separation, reduced distillation exergy destruction by 22% over 18 months, equivalent to annual natural gas savings of approximately 45 GWh.

Iron, Steel, and Metals

KPI	Below Average	Average	Above Average	Top Quartile
Blast Furnace Exergetic Efficiency	<35%	35-42%	42-48%	>48%
EAF Exergetic Efficiency	<42%	42-50%	50-58%	>58%
Waste Heat Recovery Rate (% of available exergy)	<20%	20-35%	35-50%	>50%
Specific Entropy Generation (kJ/K per tonne liquid steel)	>3,200	2,400-3,200	1,800-2,400	<1,800
Slag Enthalpy Recovery (%)	<5%	5-15%	15-30%	>30%

UK steel production, concentrated at Tata Steel's Port Talbot works and British Steel's Scunthorpe site, operates blast furnaces with exergetic efficiencies in the 38 to 44% range. The thermodynamic argument for electric arc furnace (EAF) steelmaking extends beyond direct emissions reduction: EAF processes achieve 15 to 20 percentage points higher exergetic efficiency because they avoid the massive irreversibilities associated with coke combustion and iron ore reduction. Celsa Steel's Cardiff EAF plant, operating on recycled scrap, demonstrates exergetic efficiencies of 52 to 56%, representing the UK's strongest performance in metals sector thermodynamic efficiency.

Buildings and HVAC

KPI	Below Average	Average	Above Average	Top Quartile
Heating System Exergetic Efficiency	<4%	4-8%	8-14%	>14%
Heat Pump Exergetic Efficiency (COP/COP_Carnot)	<30%	30-42%	42-55%	>55%
Cooling System Exergetic Efficiency	<12%	12-20%	20-28%	>28%
Ventilation Exergy Destruction (kWh/m2/yr)	>18	12-18	7-12	<7
Thermal Storage Round-Trip Exergetic Efficiency	<45%	45-60%	60-75%	>75%

Building heating systems represent the most egregious misuse of exergy in the UK economy. Burning natural gas at 1,800 degrees Celsius to heat water to 60 degrees Celsius and spaces to 20 degrees Celsius yields first-law efficiencies of 90%+ but exergetic efficiencies of only 4 to 8%. The UK Building Research Establishment calculates that the nation's 28 million homes destroy approximately 350 TWh of exergy annually through this thermodynamic mismatch. Heat pumps fundamentally improve this picture by upgrading low-grade environmental heat rather than degrading high-grade chemical energy. The Passivhaus Trust's monitoring of 200 UK heat pump installations found that best-in-class air source systems achieve 50 to 55% of theoretical Carnot performance, representing a fourfold improvement in exergetic efficiency compared to gas boilers.

Food and Beverage Processing

KPI	Below Average	Average	Above Average	Top Quartile
Drying Process Exergetic Efficiency	<12%	12-20%	20-30%	>30%
Refrigeration COP/COP_Carnot Ratio	<25%	25-38%	38-50%	>50%
Steam System Exergetic Efficiency	<22%	22-32%	32-42%	>42%
Heat Integration Achievement (% of pinch target)	<40%	40-55%	55-70%	>70%
Overall Site Exergetic Efficiency	<15%	15-22%	22-30%	>30%

Drying operations, used extensively across dairy, bakery, and beverage ingredient manufacturing, are the single largest source of exergy destruction in food processing. Conventional spray dryers operate at 15 to 20% exergetic efficiency, with the majority of losses occurring through exhaust gas rejection and evaporative irreversibilities. Nestlé's Dalston factory in Cumbria achieved a 35% reduction in drying-related exergy destruction by implementing heat pump-assisted closed-loop drying, recovering latent heat from exhaust moisture and reinjecting it into the process air stream. The Carbon Trust's Industrial Decarbonisation programme identified that UK food manufacturers could collectively recover 8 to 12 TWh annually through systematic application of pinch analysis to thermal processes.

Meaningful Metrics Versus Vanity Metrics

Meaningful: Exergetic efficiency by process unit. This reveals where thermodynamic value is destroyed and points directly to intervention opportunities. A process unit with 15% exergetic efficiency operating in a plant averaging 35% signals a high-priority target for improvement.

Vanity: Overall energy intensity (kWh per tonne of product) without thermodynamic decomposition. While useful for benchmarking, energy intensity conflates thermodynamically unavoidable minimum energy requirements with reducible irreversibilities. Two plants with identical energy intensity may have radically different improvement potential depending on how close each operates to the thermodynamic minimum.

Meaningful: Entropy generation rate by equipment or process stage. This metric quantifies the thermodynamic cost of each operation and enables ranking of improvement priorities by physical impact rather than subjective assessment.

Vanity: Percentage improvement year-over-year without reference to theoretical limits. A plant improving energy intensity by 2% annually sounds impressive until analysis reveals it operates at 25% exergetic efficiency with a theoretical minimum of 65%, meaning over 60% of the improvement potential remains untapped.

Meaningful: Heat integration achievement as a percentage of pinch analysis target. This measures how effectively a site recovers internal heat relative to the thermodynamically optimal configuration, providing a clear gap analysis for capital planning.

Vanity: Total waste heat recovery in absolute terms (MWh recovered) without reference to available exergy. Recovering large quantities of very low-grade waste heat (below 60 degrees Celsius) may look impressive in energy terms while contributing minimal useful work, because the exergy content of low-temperature heat is small.

Action Checklist

• Commission an exergy audit of your primary production processes, focusing on the five largest energy-consuming operations
• Calculate entropy generation rates for individual process units to identify the top three sources of thermodynamic loss
• Conduct or update a pinch analysis for your site's thermal processes and benchmark heat integration achievement against the theoretical target
• Replace or supplement first-law energy intensity KPIs with exergetic efficiency metrics in internal performance dashboards
• Evaluate heating systems using exergetic efficiency rather than first-law efficiency to properly assess the thermodynamic case for heat pump adoption
• Assess system-level complexity before implementing local efficiency improvements to anticipate unintended consequences
• Benchmark your sector-specific KPIs against the ranges in this article to identify performance gaps and priority improvement areas
• Include exergy-based metrics in SECR and ISSB disclosures to demonstrate thermodynamic rigour beyond standard carbon reporting

FAQ

Q: What is the practical difference between energy efficiency and exergy efficiency, and why does it matter? A: Energy efficiency measures how much energy output you get relative to energy input, but it treats all forms of energy as equivalent. Exergy efficiency accounts for the quality of energy, recognising that electricity and high-temperature heat have far greater work potential than low-grade warmth. A gas boiler may be 92% energy efficient but only 6% exergy efficient because it converts high-quality chemical energy into low-quality heat. This distinction matters because exergy analysis reveals the true thermodynamic improvement potential that first-law analysis misses.

Q: How do I conduct an exergy audit without specialised thermodynamics expertise? A: Start with your existing energy audit data and apply published exergy factors for common utility streams (steam at various pressures, electricity, cooling water, compressed air). The Carbon Trust and the UK Energy Research Centre publish sector-specific guidance. For more detailed process-level analysis, engage a specialist engineering consultancy with thermodynamic modelling capability. Initial screening-level exergy audits typically cost 15,000 to 40,000 GBP for a medium-sized industrial site.

Q: Are these KPIs relevant for service-sector organisations or only heavy industry? A: Buildings KPIs apply directly to offices, hospitals, universities, and retail premises. Any organisation with significant heating, cooling, or ventilation loads benefits from exergetic analysis. The thermodynamic case for heat pumps, for example, is most clearly understood through exergy metrics. Service-sector organisations consuming more than 500 MWh annually should consider building-level exergy assessment.

Q: How do thermodynamic KPIs relate to carbon reporting and net zero targets? A: Every unit of exergy destroyed represents energy that must be supplied from external sources, carrying associated carbon emissions. Reducing exergy destruction directly reduces primary energy demand and, consequently, emissions. Thermodynamic KPIs provide a physics-based foundation for setting reduction targets that are ambitious but achievable, grounded in the gap between current performance and theoretical limits rather than arbitrary percentage goals.

Q: What is the typical payback period for investments identified through exergy analysis? A: Heat integration improvements identified through pinch analysis typically deliver paybacks of 1 to 3 years. Process modifications targeting high entropy generation rates (such as distillation column retrofits or heat pump integration) deliver paybacks of 2 to 5 years. Building-level interventions such as heat pump installation show paybacks of 5 to 8 years at current UK energy prices, improving to 3 to 5 years with available government incentives.

Sources

• UK Climate Change Committee. (2025). Progress in Reducing Emissions: 2025 Report to Parliament. London: CCC.
• UK Energy Research Centre. (2024). Exergy Analysis of UK Industrial Energy Systems: Identifying Hidden Waste. London: UKERC.
• Carbon Trust. (2025). Industrial Decarbonisation: Thermodynamic Opportunities in UK Manufacturing. London: Carbon Trust.
• Dincer, I. and Rosen, M.A. (2024). Exergy: Energy, Environment and Sustainable Development. 4th edition. Amsterdam: Elsevier.
• Linnhoff, B. et al. (2023). A User Guide on Process Integration for the Efficient Use of Energy. Rugby: Institution of Chemical Engineers, updated edition.
• Department for Energy Security and Net Zero. (2025). Industrial Decarbonisation Strategy: 2025 Update. London: DESNZ.
• Passivhaus Trust. (2025). UK Heat Pump Performance Monitoring: Results from 200 Installations. London: Passivhaus Trust.