Net Free-Energy Conversion Efficiency as a Unifying Metric for Food Quality

1. Introduction

1.1 The Calorie Problem

The calorie, as applied to nutrition, is a bomb calorimetry measurement: the total heat released when a food is combusted to completion in pure oxygen (Atwater, 1900). This quantity — gross energy — has dominated nutritional science for over a century. The Atwater system and its descendants assign fixed energy values to macronutrients (protein: 4 kcal/g; carbohydrate: 4 kcal/g; fat: 9 kcal/g; alcohol: 7 kcal/g) and form the basis of food labeling worldwide (FAO, 2003).

Yet the human body is not a bomb calorimeter. It does not combust food to completion. It is an open, dissipative thermodynamic system operating far from equilibrium (Prigogine, 1977; Prigogine & Nicolis, 1977), where food undergoes a cascade of coupled biochemical reactions — digestion, absorption, transport, oxidation, and biosynthesis — each with its own efficiency, each generating entropy. The first law of thermodynamics (energy conservation) constrains total energy balance but says nothing about the quality of energy conversion. The second law provides this missing dimension: it quantifies the irreversibility of metabolic processes and the thermodynamic cost of maintaining biological order.

A growing body of evidence demonstrates that the first law alone is insufficient to explain metabolic outcomes. Istfan (2025) showed that oxidative phosphorylation efficiency varies significantly between individuals (~57% mean, with meaningful inter-individual differences), and that feeding is associated with lower efficiency and higher free-energy dissipation — implying that what you eat affects not just how much energy enters the system but how efficiently it is converted. Hall et al. (2019) demonstrated in a randomized controlled trial that ultra-processed diets cause ~500 kcal/day overconsumption compared to unprocessed diets matched for macronutrients, energy density, sugar, sodium, and fiber — suggesting that food processing affects metabolic regulation through mechanisms invisible to first-law accounting.

1.2 The Second-Law Perspective

Non-equilibrium thermodynamics provides the theoretical apparatus to address this gap. The central quantity is entropy production rate (σ), which measures the rate at which a system dissipates free energy into waste — heat, disordered byproducts, and irreversible damage. For a living system, minimizing entropy production per unit of useful work is the thermodynamic definition of efficiency.

Prigogine (1977) established that living organisms are dissipative structures: ordered systems maintained far from equilibrium by continuous free-energy throughput. The organism takes in low-entropy inputs (food, oxygen) and exports high-entropy outputs (CO₂, heat, waste). The difference — the entropy produced — is the thermodynamic price of life. Silva and Annamalai (2008) applied this framework quantitatively, computing lifetime entropy generation for humans from metabolic data and predicting life spans of 73.78 years (male) and 81.61 years (female) from entropy generation rates alone — values within 2% of actuarial statistics.

The implication is direct: if lifetime entropy generation is approximately constant, then the rate of entropy production determines life span. And the rate of entropy production is partly determined by diet — both through the efficiency of metabolic conversion and through the secondary entropy costs of oxidative stress, inflammation, and metabolic waste.

1.3 Scope and Contribution

This paper proposes a unified framework — the Thermodynamic Food Rating (TFR) — that evaluates food by its net free-energy conversion efficiency. We:

1. Derive a theoretical expression for food-level thermodynamic efficiency (TFR_theory) from first principles of non-equilibrium thermodynamics, using the Kedem-Caplan degree-of-coupling formalism as extended by Stucki (1980) and Wikström & Springett (2020), and derive from it an operational estimator (TFR_op) using available proxy measurements.
2. Decompose the entropy-production cost of food into five components, three grounded in established literature and two proposed as novel contributions.
3. Present preliminary TFR scores for representative foods.
4. Generate testable predictions.

We do not claim that TFR should replace existing nutritional metrics. We argue that it should complement them by adding the dimension that first-law quantities miss: the thermodynamic cost of converting food into useful work.

2. Theoretical Framework

2.1 The Body as a Non-Equilibrium Energy Converter

We model the human body as a coupled non-equilibrium energy converter in the sense of Kedem and Caplan (1965). The fundamental process is:

Input force (X₂): oxidation of food substrates (characterized by the redox potential, ΔG_ox)
Output force (X₁): phosphorylation of ADP to ATP (characterized by the phosphorylation potential, ΔG_p)
Coupling: achieved through the proton-motive force across the inner mitochondrial membrane, mediated by complexes I, III, and IV of the electron transport chain plus ATP synthase.

In the linear non-equilibrium thermodynamic (LNET) regime, the phenomenological equations are:

where J₁ is the ATP synthesis flux, J₂ is the oxygen consumption flux, and L_ij are the Onsager phenomenological coefficients satisfying the reciprocal relation L₁₂ = L₂₁.

The degree of coupling is defined as:

where q ranges from 0 (fully uncoupled) to 1 (fully coupled). Kedem and Caplan (1965) showed that the maximum efficiency of energy conversion depends solely on q:

Wikström and Springett (2020) measured the degree of coupling for the three protonmotive complexes of the mitochondrial respiratory chain during active ATP synthesis (State 3), finding q ≥ 0.99 with thermodynamic efficiencies of 75–90%. This represents the intrinsic machinery efficiency — the best the system can achieve under optimal substrate conditions.

2.2 From Intrinsic to Realized Efficiency

The intrinsic efficiency of oxidative phosphorylation (η_OXPHOS) represents the energy conversion at the mitochondrial level. But the realized efficiency of food-to-work conversion involves additional losses:

where:

• B = bioavailability coefficient (fraction of ingested food that reaches the mitochondria in oxidizable form)
• f_TEF = thermic effect of food (fraction of metabolizable energy consumed in digestion, absorption, and processing)
• f_entropy = fractional entropy cost (additional entropy production from oxidative stress, inflammation, waste processing, hormonal disruption, and microbiome effects)

2.3 The TFR Equation: Theoretical Form (TFR_theory)

We define the theoretical Thermodynamic Food Rating as the ratio of useful biological work to exergy input:

where:

• W_useful = useful work extracted = Ex_food × B × η_OXPHOS × (1 − f_TEF) × (1 − f_extra)
• Ex_food = exergy content of the food (kJ, for a defined portion)
• f_extra = fractional exergy loss from diet-attributable entropy-production channels beyond baseline OXPHOS irreversibility

Expanding f_extra:

where R̃, Ĩ, W̃ are exergy fractions lost to excess ROS damage, inflammatory response, and waste processing respectively, and w_R, w_I, w_W are weighting coefficients to be determined empirically.

For a "perfect" food — fully bioavailable, minimal thermic effect, no excess ROS, no inflammation, no waste beyond CO₂ and H₂O — f_extra = 0 and TFR_theory approaches B × η_OXPHOS × (1 − f_TEF). With η_OXPHOS ≈ 0.57 (whole-body; Istfan, 2025), B ≈ 0.95, and f_TEF ≈ 0.05, this ceiling is approximately 0.51. In practice, all foods fall below this.

Note on units: TFR_theory is dimensionless (kJ/kJ). All terms are exergy fractions for a defined portion, not rates. This avoids the dimensional inconsistency that would arise from mixing exergy stocks (kJ) with entropy production rates (kJ/K·s) in the denominator.

2.4 The TFR Equation: Operational Estimator (TFR_op)

Because f_extra cannot yet be measured in thermodynamic units for individual foods, we define an operational estimator using available proxy indices:

where:

• A = normalized ATP yield efficiency (glucose baseline = 1.0)
• B = bioavailability coefficient (0–1)
• η_ref = reference OXPHOS efficiency (fixed at 0.57 for population-level scoring)
• T = thermic effect fraction (0–0.3)
• I, R, W = normalized proxy scores for inflammatory, oxidative, and waste costs (0–1 each; see §4.2 for derivation)
• w_I, w_R, w_W = empirical weights (set to 1.0 in preliminary scoring; calibration protocol in §9.1)

The denominator (1 + weighted costs) is a heuristic penalty function, not a thermodynamic identity. It ensures TFR_op decreases monotonically as entropy-production proxies increase, with a baseline of 1 when all proxy costs are zero. The relationship between TFR_op and TFR_theory is approximate:

This approximation holds when f_extra is small (< 0.3), expected for most non-pathological foods. Validation of this mapping is a priority for empirical work (§9.1).

2.5 Exergy Content of Food

The exergy of a food quantifies its maximum work potential. For macronutrients, exergy closely tracks metabolizable energy but is not identical:

where ME is metabolizable energy and β is the exergy-to-energy ratio. For most macronutrients, β ≈ 1.0. For fats, β is slightly > 1.0 because fats are more chemically reduced (lower oxidation state) and thus contain more chemical exergy per unit of enthalpy (Çengel et al., 2018).

2.6 ATP Yield as a Function of Macronutrient

Livesey (1984) established definitive values for cytoplasmic ATP equivalents per MJ of metabolizable energy:

The range within each macronutrient reflects uncertainty in mitochondrial proton stoichiometries. The key result is that fat and carbohydrate are roughly comparable in ATP yield per unit of metabolizable energy, while protein is systematically lower due to the energetic cost of nitrogen disposal via the urea cycle.

Using current P/O ratios of 2.5 (NADH) and 1.5 (FADH₂), the net ATP yield from complete oxidation of glucose is ~30–32 molecules, and from palmitate is ~106 molecules (but palmitate weighs 3.4× more per molecule).

2.7 The Protein Dual-Mode Problem

Protein occupies a unique position in this framework. As a fuel, it is the least efficient macronutrient: lowest ATP yield per MJ, highest thermic effect (20–30% vs. 0–3% for fat), and significant waste processing cost (urea synthesis: 4 high-energy phosphate bonds per urea molecule; ≥40.3 kJ/g excreted nitrogen; Anand & Anand, 1993; van Milgen et al., 2021).

However, protein's primary biological role is not fuel but structure — the maintenance and repair of ordered biological architecture. We address this by defining two modes:

• Fuel-TFR: efficiency of a food as an energy source (applies to all macronutrients)
• Structure-TFR: efficiency of a food in maintaining biological order (applies primarily to protein, and to specific micronutrients)

This dual-mode scoring reflects the thermodynamic reality that the body is not merely an engine (converting fuel to work) but a self-maintaining dissipative structure (converting materials into ordered components while exporting entropy). In the language of biological thermodynamics: the body needs both exergy flow (fuel) and negentropy maintenance (structure).

3. The Five Entropy-Production Components

3.1 Oxidative Stress (Ṣ_ROS) — Established

Definition: The entropy generated by reactive oxygen species (ROS) produced as byproducts of electron transport and amplified by specific dietary inputs.

Mechanism: Approximately 0.2–2% of electrons traversing the mitochondrial electron transport chain escape to form superoxide radicals (O₂⁻), which generate hydrogen peroxide (H₂O₂) and hydroxyl radicals (·OH). These ROS damage lipids, proteins, and DNA — including the mitochondrial DNA encoding ETC components — creating a positive feedback loop: damaged mitochondria produce more ROS per ATP, accelerating the degradation of conversion efficiency (PMC11203720, 2024).

Measurement:

• F2-isoprostanes (F2-IsoPs): Gold-standard biomarker of lipid peroxidation. Measured by mass spectrometry. Urine baseline: 1200±600 pg/mL; plasma: 45.1±18.4 pg/mL (Milne et al., 2007). Important methodological caveat: UGT enzymes metabolize F2-IsoPs, and dietary/pharmacological factors influence UGT activity, potentially biasing unmetabolized F2-IsoP measurements (Milne et al., 2024).
• Malondialdehyde (MDA): Lipid peroxidation marker, measurable by TBARS assay.
• 8-hydroxy-2'-deoxyguanosine (8-OHdG): Oxidative DNA damage marker.
• Oxidized LDL (ox-LDL): Measured by ELISA.

Dietary modulation (evidence):

• Ultra-processed food consumption is associated with higher oxidative stress markers in adults with metabolic syndrome (PMC10451674, 2023).
• Mediterranean diet intervention significantly reduced F2-isoprostanes, ox-LDL, malondialdehyde, and methylglyoxal (PMC8113044, 2021).
• Specific foods contain compounds that reduce existing ROS (e.g., anthocyanins in blueberries, EGCG in green tea, sulforaphane in broccoli), yielding a negative Ṣ_ROS contribution — the food actively lowers the system's entropy production rate.

Thermodynamic interpretation: ROS damage to the ETC directly reduces the degree of coupling (q) in the Kedem-Caplan framework, lowering η_max. Each unit of ETC damage shifts the system from State 3 toward State 4 behavior, where q drops substantially (Wikström & Springett, 2020). The entropy cost is thus both direct (damage repair requires energy) and indirect (reduced future conversion efficiency).

Quantitative status: F2-IsoP measurement is mature and standardized. The mapping from F2-IsoP levels to entropy production rate in kJ/K requires further work but is constrained by known thermodynamic relationships.

3.2 Inflammatory Load (Ṣ_inflammation) — Established Measurement, Novel Framing

Definition: The entropy generated by the pro-inflammatory or anti-inflammatory effects of dietary components, measured through their impact on systemic inflammatory biomarkers.

Measurement:

• Dietary Inflammatory Index (DII): Literature-derived score based on 1,943 qualifying articles, scoring 45 food parameters against 6 inflammatory biomarkers (IL-1β, IL-4, IL-6, IL-10, TNF-α, CRP). Range: −4.98 (maximally anti-inflammatory) to +4.69 (maximally pro-inflammatory). Developed by Shivappa et al. (2014); standardized against a global reference database from 11 countries.
• Construct validation: Significant association with CRP, IL-6, and TNFα-R2 in the Women's Health Initiative (n=2,567 postmenopausal women; PMC4433562); elevated CRP odds ratio 1.12 at age 70 in the Lothian Birth Cohort (PMC6675764); IL-6 correlation in Japanese JPHC study (PMID 31574409).
• Empirical DII (EDII): Alternative approach using reduced rank regression in the Nurses' Health Study (n=5,230), identifying 18 food groups predicting CRP, IL-6, and TNFα-R2. Quintile 5 vs. 1 showed +60% CRP increase (PMC4958288).
• Food Inflammation Index (FII, 2024): Newer per-food scoring revealing heterogeneity within food groups (PMID 39401693).

Dietary examples:

Novel contribution: We propose that systemic inflammation represents entropy production through multiple mechanisms: (a) energy diversion to immune activation (neutrophil respiratory burst, cytokine synthesis, acute-phase protein production); (b) tissue damage requiring repair (additional biosynthetic cost); (c) signaling disruption (reduced precision of metabolic regulation = increased disorder). The Istfan (2025) finding that metabolic disorder reduces OXPHOS efficiency provides indirect support: inflammation is a major source of metabolic disorder.

Quantitative status: The DII is well-validated as a dietary-inflammatory score. The explicit thermodynamic interpretation — that DII can be mapped to an entropy generation rate — is our novel contribution and requires empirical validation. The mapping would take the form:

where k_infl is a scaling constant to be determined experimentally.

3.3 Metabolic Waste Processing (Ṣ_waste) — Established

Definition: The entropy generated by processing and excreting metabolic byproducts, primarily from protein catabolism (urea synthesis) and Maillard reaction products (advanced glycation end-products, AGEs).

Urea cycle energetics (established biochemistry):

• Cost: 3 ATP → 2 ADP + AMP per molecule of urea (4 high-energy phosphate bonds)
• Energy cost per gram of nitrogen excreted: ≥40.3 kJ/g N (Anand & Anand, 1993; van Milgen et al., 2021)
• NADH recovery: 2 NADH partially offset cost (~5 ATP equivalent), but recovery is context-dependent and unavailable during active gluconeogenesis
• This cost is the primary reason protein yields 6.4–13.2 mol ATP/MJ vs. 9.0–14.7 for glucose (Livesey, 1984)

AGE processing (established mechanism, developing quantification):

• Dietary AGEs (dAGEs): Database of ~500 foods established by Uribarri et al. (2010). Average intake: ~14,700 AGE kU/day in healthy New York adults.
• Dry heat promotes AGE formation by 10–100× above uncooked state. Animal-derived, high-fat, high-protein foods are AGE-rich; carbohydrate-rich foods (vegetables, fruits, whole grains) contain relatively few AGEs even after cooking.
• AGE detoxification requires receptor-mediated endocytosis (RAGE, AGE-R1/R2/R3) and enzymatic degradation — metabolic work that contributes to entropy production.
• Important caveat: A 2017 Advances in Nutrition perspective questioned whether ELISA-based dAGE measurements accurately reflect bioavailable AGE load, as UPLC-MS analysis found no evidence of elevated AGE levels in Western fast foods relative to other foods. The measurement methodology is under active revision.

Thermodynamic interpretation: The urea cycle cost is directly measurable in ATP equivalents and is textbook thermodynamics. The AGE processing cost is mechanistically sound but less precisely quantified at the per-food level.

3.4 Hormonal Disruption (Ṣ_hormonal) — Novel Contribution

Definition: The entropy generated when dietary inputs disrupt hormonal signaling — primarily insulin sensitivity, cortisol dynamics, and satiety hormone regulation — reducing the precision of metabolic control systems.

This component is a novel contribution of this framework. While the individual phenomena are well-documented, their packaging as a thermodynamic entropy cost of food has not been previously proposed.

Insulin resistance and metabolic efficiency

• Insulin sensitivity directly modulates the thermic effect of food: insulin-sensitive individuals show significant TEF (5–10% for carbohydrate, 20–30% for protein); insulin-resistant individuals show negligible TEF (Westerterp, 2004; PubMed 31021710).
• The HOMA-IR index (fasting glucose × fasting insulin / 405) is a validated clinical measure.
• High-glycemic diets promote insulin resistance through repeated supraphysiological insulin secretion, creating a positive feedback loop.

Satiety dysregulation

• Hall et al. (2019) demonstrated ~508 kcal/day overconsumption in a matched RCT (n=20, crossover design, Cell Metabolism). This occurred despite matched macronutrients and energy density, indicating disrupted appetite regulation independent of compositional factors.
• Overconsumption = energy input beyond efficient conversion capacity = excess entropy production.

Cortisol-metabolism coupling

• Cortisol counteracts insulin by reducing GLUT4 translocation, increasing hepatic gluconeogenesis, and reducing peripheral glucose utilization.
• Diet-induced inflammation elevates cortisol through the HPA axis, creating a cross-link between Components 2 and 4.

Measurable biomarkers: HOMA-IR, TyG index (Ln(fasting TG × fasting glucose) / 2), salivary/hair cortisol, leptin/ghrelin ratios.

Thermodynamic interpretation: A control system with reduced precision operates at lower thermodynamic efficiency — it cannot allocate resources as accurately, leading to misallocation (overconsumption, inappropriate storage, failed repair). In information-theoretic terms, hormonal disruption reduces the mutual information between metabolic state and metabolic response, which is equivalent to increased entropy in the control channel. While this interpretation is novel, it is consistent with the Istfan (2025) observation that individual variation in OXPHOS efficiency has measurable metabolic consequences.

Quantitative status: Biomarkers are well-validated. The mapping from HOMA-IR or TyG to an entropy generation rate in kJ/K is not established. This requires empirical investigation.

3.5 Microbiome Entropy (Ṣ_microbiome) — Novel Contribution

Definition: The entropy generated when dietary inputs disrupt gut microbiome diversity and function, reducing nutrient extraction efficiency and increasing systemic inflammation through gut-barrier compromise.

This component is a novel contribution. The term "microbiome entropy" uses "entropy" in both the information-theoretic sense (Shannon diversity) and the thermodynamic sense (metabolic disorder), and we argue these are connected but acknowledge the bridge is not yet fully established.

Dysbiosis indices

• Shannon entropy / alpha diversity: standard ecological measure, widely applied to gut microbiome. Higher diversity generally correlates with resilience and health (Mosca et al., 2021; PMC8208139).
• Bray-Curtis dysbiosis score: median dissimilarity between a test sample and a healthy reference population (Lloyd-Price et al.).
• Gut Microbiome Wellness Index 2 (GMWI2): stool metagenome-based health predictor, robust across external validation datasets (PMC11358288, 2024).

Diet-microbiome indices

• Dietary Index for Gut Microbiota (DI-GM, 2024): literature-derived score linking specific foods to microbiome outcomes. Beneficial: fermented dairy, whole grains, fiber, avocado, broccoli, coffee, green tea. Unfavorable: refined grains, red meat, processed meat, >40% fat.

Functional consequences of dysbiosis

• Dysbiosis → increased intestinal permeability → lipopolysaccharide (LPS) translocation → systemic inflammation (well-established cascade).
• Reduced microbiome diversity → reduced capacity for short-chain fatty acid (SCFA) production → reduced colonocyte energy supply → further barrier compromise.
• Ultra-processed food consumption linked to reduced microbiome diversity.

Thermodynamic interpretation: A diverse microbiome represents a larger metabolic toolkit — more enzymatic pathways for nutrient extraction, SCFA production, vitamin synthesis, and xenobiotic metabolism. Loss of diversity reduces this toolkit, meaning less useful work is extracted from the same food input. Additionally, dysbiosis-driven LPS translocation directly increases Ṣ_inflammation, creating a cross-term between Components 2 and 5.

Quantitative status: This is the least quantitatively grounded of the five components. Shannon diversity is measured in bits (information entropy), not kJ/K (thermodynamic entropy). The quantitative bridge — how many kJ of metabolic cost does each bit of lost microbiome diversity impose? — has not been established. The DI-GM provides a diet-to-microbiome mapping, but the microbiome-to-metabolic-cost mapping requires further research.

4. Methods: TFR Score Derivation

4.1 Data Sources

4.2 Normalization Procedure

To combine heterogeneous measurements into a single score, each component was normalized to a [0, 1] scale:

1. ATP efficiency (A): Normalized to glucose baseline. A_glucose = 1.0; other foods scaled proportionally to their mol ATP / MJ ME relative to glucose midpoint (11.85 mol/MJ).
2. Bioavailability (B): Estimated from digestibility data. For carbohydrates, Rodriguez-Illera et al. (2017) found a strong linear correlation (R² = 0.96) between glycemic index and metabolic efficiency for cooked starch sources, which we use as a proxy for metabolic bioavailability. GI formally measures digestion rate rather than absorption completeness, but for cooked starches these are tightly coupled — fast-digested starch is fast-absorbed starch. The proxy is less reliable for foods where digestion rate and absorption diverge (e.g., resistant starch). For proteins, DIAAS (Digestible Indispensable Amino Acid Score) was used where available.
3. TEF cost (T): Fractional thermic effect (0.0 to 0.3) derived from published macronutrient-specific values.
4. Inflammatory cost (I): The DII was designed as a whole-diet score. For per-food scoring, we extract food-specific inflammatory effect weights from the DII literature-review coefficients (Shivappa et al., 2014) and supplement with per-food scores from the Food Inflammation Index (Wang et al., 2024) where available. Normalized to [0, 1]. This per-food decomposition is an approximation; interaction effects between foods in a whole diet are not captured.
5. ROS index (R): Semi-quantitative ordinal estimate (0 = antioxidant-rich / ROS-reducing; 0.5 = neutral; 1.0 = high oxidant load) based on published antioxidant capacity data (ORAC values), AGE content from Uribarri et al. (2010), and known pro-oxidant properties. This is the least quantitatively grounded proxy (§9.2).
6. Waste cost (W): Estimated from protein content (urea cycle cost per gram protein catabolized), plus AGE content for cooked foods.

4.3 Composite Score Calculation

Using the operational estimator defined in §2.4:

with η_ref = 0.57 and all weights w = 1.0 for preliminary scoring. The numerator approximates useful work extracted (as an exergy fraction). The denominator is a heuristic penalty: 1 (baseline) + proxy costs. When all proxy costs are zero, TFR_op reduces to A × B × η_ref × (1 − T), the intrinsic metabolic efficiency ceiling. The relationship to TFR_theory is discussed in §2.4.

Hormonal disruption and microbiome entropy (Components 4–5) are excluded from the current operational score due to insufficient per-food data. They are retained in the theoretical framework (§2.3) for future integration.

4.4 Limitations of Current Scoring

The current TFR_op scores are directional estimates, not precision measurements. The denominator of TFR_op is a heuristic penalty function using entropy-production proxies, not measured entropy generation rates. Specific limitations:

• The ROS index is ordinal, not quantitative. Mapping food-specific F2-IsoP generation to a continuous score requires postprandial biomarker studies that have not been conducted for most foods.
• Hormonal disruption and microbiome entropy are not included in the current quantitative score due to insufficient data.
• Cross-terms between components (e.g., inflammation → insulin resistance → reduced TEF) are acknowledged but not modeled.
• Individual variation (OXPHOS efficiency, insulin sensitivity, microbiome composition, genetic polymorphisms) is not captured by a food-level score.

5. Results

5.1 Macronutrient-Level Efficiency

Intrinsic fuel-TFR calculated as: (A_normalized × 0.57 × (1 − TEF_midpoint)) / 1.0, using η_OXPHOS = 0.57 from Istfan (2025).

Finding: Fat has the highest intrinsic fuel-TFR due to its combination of comparable ATP yield and minimal thermic effect. Protein has the lowest fuel-TFR due to compounding losses from high TEF and urea synthesis. Carbohydrate is intermediate.

This does not imply that a pure-fat diet is optimal. The body requires all three macronutrients, and protein's low fuel-TFR is offset by its high structural value (structure-TFR). The framework separates these roles.

5.2 Representative Food Ratings

Tier assignment (preliminary). Tiers provide a practical reference and are defined by TFR_op cutpoints: A+ (≥ 0.35), A (0.28–0.35), B (0.20–0.28), C (0.15–0.20), D (0.10–0.15), F (< 0.10). These cutpoints are heuristic — chosen to produce a distribution consistent with existing nutritional consensus (Mediterranean-style foods cluster A/A+, ultra-processed foods cluster D/F) and will be refined when empirical calibration data become available (§9.1). Every quantitative scoring system in nutrition uses heuristic tiers (NutriScore, NOVA, NRF); the difference here is that the underlying continuous score is transparent and the tier boundaries are explicitly provisional.

*Blueberries receive R = 0.00 because their high anthocyanin content actively reduces systemic ROS, offsetting any ROS generation from their own metabolism.

5.3 Effect of Cooking Method

The same food drops from TFR_op = 0.40 (A+) to 0.18 (C) — a 55% reduction — based solely on cooking method, primarily through AGE formation (Uribarri et al., 2010: dry heat increases AGEs 10–100× above uncooked state) and lipid oxidation from the frying oil.

5.4 Exergy Efficiency Comparison with Rodriguez-Illera et al. (2017)

Rodriguez-Illera et al. found that cooked potatoes had the highest overall exergy efficiency among carbohydrate-rich staple foods when combining processing chain losses and metabolic efficiency. Our TFR_op analysis concurs: boiled potato scores 0.40 (near the theoretical ceiling) primarily due to high bioavailability and low entropy-proxy cost.

Their finding that spaghetti had low overall exergy efficiency despite low processing losses — because its low bioavailability reduces metabolic efficiency — validates our inclusion of bioavailability as a critical numerator term.

6. Discussion

6.1 What TFR Adds to Existing Frameworks

TFR integrates across these dimensions by asking a single question: how much useful work does the body extract from this food per unit of total thermodynamic cost? This is not a replacement for any existing tool but a unifying framework that subsumes their insights under a coherent physical theory.

6.2 The Entropy Cost as the Missing Variable

The most novel claim of this framework is that the entropy cost of a food — its oxidative, inflammatory, and waste-processing burden — may be as important as its energy content in determining health outcomes.

Consider two foods with identical caloric content and macronutrient profiles:

• Food A: Low DII (−0.5), low AGE content, rich in antioxidants
• Food B: High DII (+0.5), high AGE content, pro-oxidant

First-law analysis treats these as equivalent. TFR analysis shows Food A delivers more net useful work because its lower entropy cost means less of the converted energy is diverted to damage repair, immune activation, and waste processing. Over time, this difference compounds: the individual consuming Food B accumulates entropy at a higher rate, accelerating the degradation of metabolic machinery.

This aligns with Silva and Annamalai's (2008) finding that lifetime entropy generation is approximately constant at ~11,404 kJ/K per kg body mass. If this entropy budget is spent faster through high-entropy-cost diets, the implication is reduced health span and life span.

6.3 Convergence with Existing Evidence

Mediterranean diet health benefits: The Mediterranean diet scores DII = −3.98 (Shivappa et al., 2014), is rich in EVOO (low TEF, anti-inflammatory), fatty fish (anti-inflammatory omega-3), vegetables (antioxidant, anti-inflammatory), and uses moist cooking methods (low AGE formation). TFR predicts this diet would have high net efficiency and low entropy cost — consistent with its observed association with reduced cardiovascular disease, cancer, and all-cause mortality.

Ultra-processed food harm: Hall et al. (2019) showed UPF causes overconsumption independent of macronutrients. TFR interprets this as hormonal disruption (Component 4): UPF disrupts satiety signaling, causing energy input to exceed efficient conversion capacity. The excess input generates entropy without proportional useful work.

Caloric restriction benefits: Caloric restriction extends life span in multiple model organisms. TFR interpretation: reduced energy throughput at maintained OXPHOS efficiency means less absolute entropy production per unit time, extending the entropy budget.

Cooking method effects: The association between grilled/charred meat and cancer risk is explained by Component 3: high-temperature cooking generates AGEs and heterocyclic amines (HCAs), increasing waste processing cost and ROS load.

6.4 The Protein Problem Resolved

Traditional nutritional frameworks struggle with protein because it is simultaneously essential and metabolically expensive. TFR resolves this through dual-mode scoring:

• As fuel (fuel-TFR): protein is the least efficient macronutrient due to compounding losses from high TEF and urea synthesis.
• As structure (structure-TFR): protein is the most valuable macronutrient because maintaining biological order (Preservation in the EDROP framework) requires continuous amino acid supply.

The practical implication: eat protein for structure, not for fuel. The amount of protein consumed should match structural needs (maintenance, repair, growth), not energy needs. Excess protein beyond structural requirements is catabolized at high thermodynamic cost.

This aligns with the observation that moderate protein intake (~0.8–1.6 g/kg/day) is associated with optimal health outcomes, while very high protein diets (>2.0 g/kg/day) show diminishing returns — the structural needs are met, and excess protein pays the urea penalty without additional structural benefit.

7. Testable Predictions

8. Limitations

8.1 Quantitative Limitations

The current TFR scoring relies on mixed data quality. Components 1–3 (ROS, inflammation, metabolic waste) have validated measurement instruments with published per-food data. Components 4–5 (hormonal disruption, microbiome entropy) have validated biomarkers but lack per-food quantification. The entropy generation rate mapping (Ṣ in kJ/K) is established at the whole-body level (Silva & Annamalai, 2008) but not at the per-food level for most components.

8.2 Individual Variation

OXPHOS efficiency varies significantly between individuals (Istfan, 2025). Insulin sensitivity modulates TEF from significant to near-zero. Gut microbiome composition varies by orders of magnitude between individuals. Genetic polymorphisms in detoxification enzymes (CYP450, GST, UGT) affect the entropy cost of waste processing. A universal food-level TFR is therefore necessarily approximate. Personalized TFR, adjusting for individual metabolic phenotype, is the long-term goal but requires metabolic profiling infrastructure that does not yet exist at scale.

8.3 Context Dependence

The TFR of a food depends on:

• Metabolic state: Fasted vs. fed, resting vs. exercising
• Combination effects: Fat increases fat-soluble vitamin absorption; fiber modulates glycemic response; phytates reduce mineral bioavailability; vitamin C enhances iron absorption
• Temporal context: Circadian variation in metabolic efficiency
• Dose: The dose-response curve is non-linear for many entropy-cost components

8.4 Measurement Methodology and Proxy Limitations

Several proxy choices in the current TFR_op scoring introduce known approximation errors:

• GI as bioavailability proxy: Rodriguez-Illera et al. (2017) found R² = 0.96 between GI and metabolic efficiency for cooked starches — a strong empirical basis. GI formally measures digestion rate, not absorption completeness, but for cooked starches these are tightly coupled. The proxy weakens for resistant starch or foods where digestion/absorption diverge. Isotope tracer studies would provide ground-truth bioavailability but are not available for most foods.
• Per-food DII decomposition: The DII was validated as a whole-diet score. Our per-food decomposition extracts individual food coefficients from the DII literature weights, supplemented by the Food Inflammation Index (Wang et al., 2024). This ignores food-food interaction effects in inflammatory response.
• ROS index: The R score is semi-quantitative (ordinal), not derived from postprandial F2-IsoP measurements. Systematic postprandial biomarker studies for common foods (§9.2) would replace this with a continuous, empirically derived measure.
• AGE measurement: The ELISA vs. UPLC-MS debate (Advances in Nutrition, 2017) highlights that even established components have unresolved methodological questions.
• F2-IsoP confounders: UGT enzymes metabolize F2-IsoPs, and dietary/pharmacological factors influence UGT activity, potentially biasing measurements (Milne et al., 2024).

8.5 Scope Limitations

TFR evaluates food at the thermodynamic level. It does not capture:

• Psychological and social dimensions of eating
• Hedonic value and palatability
• Cost, availability, and cultural significance
• Environmental sustainability (though exergy analysis could be extended to include production-chain losses, as in Rodriguez-Illera et al., 2017)
• Individual taste, satiety, and compliance

8.6 Linearity Assumption

The LNET (linear non-equilibrium thermodynamic) framework assumes that the flux-force relationships remain approximately linear in the physiological operating range. Stucki (1980) experimentally verified linearity for oxidative phosphorylation in the range of output forces of practical interest, and Istfan (2025) confirmed this for human whole-body metabolism. However, pathological states (severe insulin resistance, advanced mitochondrial dysfunction) may push the system into the non-linear regime, where the formalism would need extension.

9. Future Work

9.1 Weight Calibration and Validation Strategy

The operational estimator TFR_op contains three free weights (w_I, w_R, w_W) currently set to 1.0. Two complementary calibration strategies are proposed:

Strategy A provides a population-level calibration quickly. Strategy B provides mechanistic validation. Both are needed to move TFR_op from a conceptual estimator to an empirically grounded metric.

9.2 Per-Food Entropy Profiling

Systematic postprandial biomarker studies for common foods: measure F2-IsoP, CRP, insulin response, and RQ for 2–6 hours after consuming standardized portions of individual foods, enabling empirical TFR scoring.

9.3 Personalized TFR

Develop a metabolic phenotyping protocol (OXPHOS efficiency via ketone ratio, HOMA-IR, microbiome diversity index) that allows individual calibration of TFR scores. The vision: a blood/stool test combined with dietary records yields a personalized food quality assessment.

9.4 Computational Model

Build a dynamic systems model of TFR that captures:

• Cross-terms between entropy components (inflammation → insulin resistance → reduced TEF)
• Temporal dynamics (circadian variation, long-term adaptation)
• Dose-response non-linearities
• Meal combination effects

9.5 Extension to the Food System

Rodriguez-Illera et al. (2017) demonstrated exergy analysis of the food processing chain. TFR could be extended to evaluate total exergy efficiency from farm to metabolism, providing a unified thermodynamic metric for food system sustainability.

10. Conclusion

We have presented a framework for evaluating food quality through the lens of non-equilibrium thermodynamics. The Thermodynamic Food Rating defines food quality as net free-energy conversion efficiency: the ratio of useful biological work to total exergy input, penalized by entropy-production proxy costs. The theoretical form (TFR_theory) provides the physics; the operational estimator (TFR_op) provides a computable approximation using available data. This framework integrates established biochemical data (ATP yield, thermic effect, bioavailability, oxidative phosphorylation efficiency) with entropy-production proxies (oxidative stress, inflammatory load, metabolic waste processing) and identifies two additional entropy-cost channels (hormonal disruption, microbiome entropy) for future quantification.

The core insight is that the metabolic cost of a food — beyond its caloric content — deserves systematic quantification. Two foods with identical caloric profiles can differ in their net biological utility if one imposes higher oxidative, inflammatory, and waste-processing costs. The TFR framework provides a structure for measuring this difference.

This framework does not replace existing nutritional tools. It provides a thermodynamics-informed basis for observations that compositional analysis alone cannot explain — why ultra-processed foods drive overconsumption independent of macronutrients, why cooking method affects health outcomes, why the Mediterranean diet outperforms its macronutrient profile, and why caloric restriction extends life span.

The framework is testable, the predictions are specific, and the calibration path is clear. The work that remains is empirical.

References

Appendices

Appendix A: Notation Summary

Appendix B: Derivation of η_max from Degree of Coupling

Starting from the LNET phenomenological equations (1), the thermodynamic efficiency of energy conversion is:

Defining the force ratio x = X₁/X₂ · √(L₁₁/L₂₂) and the degree of coupling q = L₁₂/√(L₁₁L₂₂), the efficiency becomes:

Maximizing η with respect to x gives the optimal force ratio:

Substituting back:

For the mitochondrial respiratory chain in State 3, q ≥ 0.99 (Wikström & Springett, 2020), giving η_max ≥ 0.80. The whole-body η_OXPHOS of ~0.57 (Istfan, 2025) reflects additional losses from proton leak, substrate transport, and the coupling between ETC-level and cellular-level energy conversion.

Appendix C: EDROP Mapping

For readers familiar with the EDROP substrate framework (Energy/Entropy, Distinction, Relation, Order, Preservation), the TFR components map directly:

The isomorphism is not coincidental. Both the TFR framework and EDROP describe systems that must convert free energy into local order while exporting entropy — the fundamental thermodynamic challenge of life.