Independent Researcher, Aarhus — Friction Theory & Behavioural Friction Theory
I work on Friction Theory: a framework for what systems do when they have to choose between alternatives under finite time and energy. The same architecture appears in brains, slime moulds, large language models, and (in the newest extension) quantum-scale physics. I study what each of those substrates can teach us about the others.
Any system that has to choose between alternatives within a finite time and energy budget runs a kind of internal race: parallel candidate-answers compete, one wins, the others are suppressed at a cost. That cost, in time, energy, information, is what I call friction. The same race-structure shows up across brains, slime moulds, transformer language models, and certain physical systems. The shared structure isn't metaphor; it's a consequence of the shared constraint. Friction Theory (Paper 1) is the substrate-universal version of the framework. Behavioural Friction Theory (Paper 0) is its biological specialisation, organised around four functional fields (Safety, Meaning, Capability, Effort).
A pattern that shows up almost everywhere
One of the strongest signatures in the framework is the inverted U: too little hurts, too much hurts, optimal performance is in the middle. It appears at almost every scale examined: qubit decoherence (10−15 s), electron drift in metals, chemical reaction rates, stochastic resonance in noisy detectors, information encoding during learning, Yerkes-Dodson arousal in whole organisms. Seven phenomena, roughly forty orders of magnitude apart in characteristic timescale, conjectured to share the same shape because they may share the same race-architecture constraint.
This has an uncomfortable implication for how we usually divide biology from physics. We tend to treat human cognition as a separate category: humans have minds, computers compute, atoms just sit there. The framework's proposal is that these are less separate than their vocabularies suggest: a human inverted U on challenge and a qubit's coherence-vs-decoherence window may share the same race-structure, differing in substrate rather than in shape. Paper 10 develops this as a unifying vocabulary, with the Schwinger-Keldysh formalism admitting a race-axiomatisation under three assumptions. It is explicitly not a claim of new physics.
Three ways to read this site:
You're here — English (technical). Formal definitions, datasets, citations, falsifiability criteria. For researchers in ML, cognitive science, neuroscience, or related fields.
English (plain). Same ideas, no jargon, with worked examples and visualisations. For science-curious general readers.
Dansk. Den danske letlæselige udgave — samme indhold på dansk.
The site has two foundation papers and a growing set of empirical and applied ones. Friction Theory (FT, Paper 1) is the substrate-universal version. Behavioural Friction Theory (BFT, Paper 0) is its biological specialisation, organised around four functional fields (Safety, Meaning, Capability, Effort). The other papers test specific empirical predictions in language models, derive consequences for clinical conditions, or extend the vocabulary toward physics-scope substrates (Paper 10).
For researchers: friction at commit step t is operationalised as Ft = −log pwinner(t) + ∑i∈losers wi·pi(t): the information-theoretic cost of selecting one route from the competing distribution, with the lower bound set by Landauer's principle (kBT ln 2 per irreversibly committed bit). The Competing Routes (CR) signal used throughout the LLM-substrate work is the operational counterpart: CR(t) counts the number of candidate tokens within probability-margin of the chosen token at position t. See Paper 1 §2 for the full derivation.
Overview pages
Findings & new explanations — what's new in this research program: empirical discoveries (three orthogonal friction axes, surprise-attention coupling, the friction ceiling, +12-21pp from friction-guided inference combined pipeline), new framework explanations for known phenomena (loss aversion as substrate-horizon commit-timing, hysteresis as learning-precondition, biases as thermodynamic necessities, surprise-vs-reactance distinction), and methodological innovations.
Cross-substrate phenomena — evidence-based mapping of 14 phenomena from human cognition observed in language models (anchoring, hysteresis, mode-shift cost, expertise reversal, and others) and a set of phenomena that depend on biological substrate-features absent in LLMs (loss aversion, between-session memory, and others). Organised by domain.
Learning — what the framework predicts and finds — dedicated treatment of learning across the paper series: hysteresis as precondition, encoding-through-loading, signal-budget redistribution, calibrated retrieval-practice, expertise reversal. Bridges human cognitive science (Bjork, Sweller, Craik & Lockhart) with empirical findings in fine-tuned LLMs.
Counterintuitive findings — why LLMs aren't calculators — the surprising things about language models: information overload, the overexplanation effect, the completeness/learnability distinction, anchoring, hysteresis, reactance, the inverted-U on challenge, confident-wrong errors, expertise reversal. Each is a structural consequence of race-architecture probabilistic computation, not a contingent property of transformers.
Papers — published preprints
The active papers, clustered by domain. Foundations (P0/P1/P6) feed the empirical and applied clusters; P10 extends the substrate scaffolding to physics-scope. All current live preprints are drawn in; P9 (in preparation) and the parked items (P11, P12) are noted in the legend.
Behavioural science has produced robust findings across dozens of research traditions but lacks the integrative architecture needed to connect them. BFT proposes friction — the cost the nervous system assigns to a potential action in a given situation — as a common currency, organised across four computational fields and five regulatory layers, with the RACE model as central mechanism. 21 formal propositions, each with empirical support and minimal test designs.
Pødenphant Lund, T. (2026b). Preprint. Target: Behavioral and Brain Sciences.
Introduces Friction Theory (FT): a substrate-universal framework treating friction as the thermodynamic cost any computational substrate pays when parallel evaluation of competing candidates resolves into a single commit. BFT ⊆ FT. Tested on 15 LLM architectures with seven cross-architecture empirical signatures, including mode-shift entry cost (Cohen d = 0.83-0.88 on instruct models; null or reversed on matched base models — an RLHF-imposed effect, not a substrate property) and surprise-attention coupling (ρ = +0.17, p < 0.0001 on Qwen2.5-0.5B). Cross-substrate validation across slime mould, C. elegans, mammals.
Pødenphant Lund, T. (2026c). Preprint. Target: PNAS Perspective.
LLMs solve two differentiable task types on the same knowledge base: cloze retrieval saturates at 8B parameters; application scales monotonically from 2% (0.5B) to 85% (70B), Spearman ρ = +1.000 on the Qwen2.5 ladder. Frontloaded in-context learning on an invented domain ("Zorbetik") eliminates pretraining-prior confounds. MoE models scale on active, not total, parameters.
Pødenphant Lund, T. (2026d). Preprint. Target: NeurIPS.
A method using the model's own logprob distribution — available at zero cost from any OpenAI-compatible API — to select calibrated correction strategies and identify questions where the model should abstain. Strategy pipeline alone yields +7.7 to +20.8 pp on four of five tested cells; combined with CR-guided 20% abstention on four cells where both were measured, the combined pipeline reaches +12 to +21 pp. On SimpleQA, the combined pipeline lifts Qwen3-235B past GPT-4o and GPT-4.1.
Pødenphant Lund, T. (2026e). Preprint. Target: Synthese.
Investigates whether FT's mathematical scaffolding extends to physics-scope substrates. Seven apparently independent phenomena — qubit decoherence, Ohm's law, molecular kinetics, stochastic resonance, Margolus-Levitin saturation, encoding-friction, Yerkes-Dodson — are conjectured to be organisable under one race-structural vocabulary across forty orders of magnitude, with a kernel-conditional inverted-U. The Schwinger-Keldysh formalism admits a race-axiomatisation under three assumptions; falsification criterion specified. No new physics. Open research program.
Pødenphant Lund, T. (2026). Preprint. Target: Foundations of Physics.
Asks the accounting question in reverse: not how fast the Born exponent follows from the full unitary group, but what the minimal mixing premise is that still forces it. For coordinate-additive rules, invariance under a single genuine two-route mixer forces g(x) = cx² whenever n ≥ 3, and polarisation reconstructs the Hermitian inner product. A trichotomy with an empty middle: generalised permutations constrain nothing. Explicitly a characterisation, not a derivation; fails at n = 2; proven for two-route mixers only.
Pødenphant Lund, T. (2026). Preprint. Target: J. Stat. Mech.
For an ideal diffusive QND measurement, the log-odds path law is exactly a Born-weighted mixture of two drifted Brownian motions on the full path σ-algebra, giving the exact time-in-lead occupation law up to localisation: an exact joint Laplace transform and a one-parameter family interpolating between an arcsine-adjacent law and Bernoulli. Exact identities include the eventual loser leading exactly half a measurement time from a symmetric start. The underlying representation is classical (Beneš, Shiryaev, Bauer–Bernard) and no priority is claimed for it; ideal case only.
Pødenphant Lund, T. (2026f). Preprint v2. Target: Emotion Review.
A substrate-grounded taxonomy of emotions integrating basic-emotions (Ekman, Plutchik, Panksepp) and constructed-emotion (Barrett) traditions. Six moving parts (friction quality, fields, layers, valence, dynamics, configurations) generate ~45 distinct feeling-labels with substrate-paths. Emotions emerge as substrate-level signals; feelings as interpretive integrations. Resolves the Panksepp–Barrett disagreement as scope-separation. Three falsification criteria with quantitative thresholds.
Pødenphant Lund, T. (2026n). Preprint. Target: Cognitive Science.
Specifies the operational mechanism by which friction is resolved in any substrate satisfying the race-axioms. Four mechanism-level components: race-opening (the threshold for initiating a race), recursive resolution (multi-scale simultaneous resolution), manifested behaviour (the route that wins becomes observable action), and thermodynamic termination (the cost of clearing the race). Behaviour is reframed as a manifested resolution-route, with implications for compulsive behaviour, OCD, tics, stress-driven habits, and burnout-trajectory as one mechanism.
Pødenphant Lund, T. (2026p). Preprint. Target: TMLR.
Why do fine-tuned LLMs hallucinate more confidently than ICL-equipped counterparts on the same knowledge? Each backward pass amplifies the winning route and presses alternatives below the noise floor; FT compresses the calibrated distribution as a structural consequence of cumulative gradient pressure. ICL preserves it. The architecture-level distinction maps onto working-memory / long-term-memory. Empirical anchor (Zorbetik, Qwen2.5-3B/7B): cloze gap 16–28 pp, log(CR_pos0) collapse 5.46→21.12, entropy→0. Generalises Paper 1's RLHF-paradox to all weight-update training.
Pødenphant Lund, T. (2026). Preprint. Target: TMLR / Cognitive Science / Trends in Cognitive Sciences.
Truth-value judgment in race-architecture substrates is implemented as the substrate's reactance signature — measurable as a discontinuous CR-collapse at the first content-token-position. Empirical anchor: cliff-event on Qwen2.5-7B + Mistral-7B-v0.3 (p < 1e-17), eleven encoding-depth checkpoints (monotonic rising in log-epoch), eight floating-point substrates (collapse = mantissa_bits × ln 2, R² = 0.9999), and a cross-domain readout test (preference vs truth, same direction, ~60% magnitude). The N400 ERP is reinterpreted as the biological-substrate readout of the same cliff-event; P14.11 specifies the direct human-subject test. Cognitive dissonance, indoctrination, and expertise reversal as special cases at high encoding-depth.
Pødenphant Lund, T. (2026q). Preprint. Target: Learning and Instruction / Cognitive Science / TMLR.
An encoding-through-loading framework: substrates encode the processing-friction generated by operating on input-friction, not the information they receive. Eight experiments on six LLM substrates (Qwen2.5 1.5B/7B/32B base, Qwen2.5-7B-Instruct, Llama-3.3-70B-Instruct, Qwen3-235B, DeepSeek-V3) on a chemistry composition task. Findings: substrate-graded U-curve in expertise-reversal (Llama-3.3-70B 75→52→61% across 0/1/3-shot); per-token CR peaks at 1-shot strategy-crossover (CR=1.114); elaborated demonstrations reduce friction (+16pp); format-violation reactance (70→48%, 22pp collapse); volume not the cost-driver (random nonsense costs 13pp across 1600× volume increase, semantically-plausible elaboration costs 20pp at 60× less volume); placement-patterns specific to trigger class. Positioned beneath the Triple-M framework (Simonsmeier & Schneider 2025) as a substrate-level mechanism.
A programmatic proposal, not a completed unification: a candidate substrate-level vocabulary under which nine independently-developed inverted-U traditions in learning theory and belief-revision research might be organised. The proposed schema is L ∝ 𝟙[|d−m| > c] · coherence(d,m) · r, read as a measurement vocabulary rather than a fully-specified predictive equation. Three-grade stratification of the nine traditions makes empirical commitments explicit: five Grade (a) re-expressions (Yerkes–Dodson, Vygotsky ZPD, Kalyuga expertise-reversal, curriculum learning, testing effect), two Grade (b) candidate derivations with novel quantitative predictions (Bjork spacing as derived temporal shadow of recovery-time τ(I); desirable difficulties' descending limb from flow-breakdown χ), two Grade (c) speculative extensions (rate-distortion as c→0 limit; reactance/dissonance as predicted biological inverted-U). The central live falsifier is the three-parameter orthogonality, not yet demonstrated on any single substrate. The original Paper 6 was restructured into a core paper plus companion Paper 6BC (consolidating the originally-planned 6B+6C; 6D dropped).
Pødenphant Lund, T. (2026r). Preprint v1 (Paper 6BC).
A programmatic proposal for two candidate substrate signatures of race-architecture, both measurable from logprobs alone on language-model substrates. Readout 1 (post-encoding trace-dominance): friction invested during encoding lays down a deeper hysteresis trace, carrying larger signal-share in subsequent comparative-evaluation races. Six classical effort-value biases (IKEA effect, endowment effect, sunk-cost fallacy, generation effect, effort justification, effort heuristic) are argued to share this race-mechanic component — carefully scoped as one component of an effort-essential subset, not a single-mechanism reduction. Endowment under passive-ownership and sunk-cost under commitment-without-effort are explicitly not explained. Readout 2 (commit-position): a preliminary probe on Qwen2.5-7B-Base vs instruct shows three direction-consistent patterns — base model 3.4× wider cross-condition commit-spread, drift away from secretary-problem 1/e ≈ 0.368 as task-interpretation deepens, recognition-commit coupling Pearson r = 0.528 (base) vs r = 0.104 (instruct). The 1/e numerical match is recorded as a coincidence to be replicated, not a finding. Three-grade taxonomy of claims; explicit accumulator-models engagement (DDM, LCA) in Appendix B.
Pødenphant Lund, T. (2026g). Preprint v1 (pilot-scale).
The empirical-calibration companion to Paper 6 on LLM substrate. Eight friction-intensity axes tested via LoRA fine-tuning Qwen2.5-7B-Instruct on fictive "Zorbetik" facts (designed to eliminate pretraining priors). Four of five intra-session axes produce inverted-U parabolas (task-friction, chunking density R²=0.89, learning-rate catastrophic cliff σ=0.019 log-units, sampling temperature R²=0.985 peak T≈0.4–0.5). The fifth axis (violation magnitude) produces a framework-narrowing null that forces a four-way consolidation taxonomy. The paraphrase-augmentation finding: same 25 facts, 1 template → 38% paraphrase-robust recall; 4 templates → 94% (+56 pp under matched substrate / optimizer / facts / epochs). The deep-vs-surface task-friction direction confirmed on 5 of 6 substrate×paradigm pairings across Qwen+Llama families and fine-tuning + in-context-learning paradigms. Pilot-scale (per-condition n=4–30); planned v2 will scale up.
Three threads of cognitive science, behavioural economics, and philosophy of mind — self-modelling, theory of mind, and free will — defended as three manifestations of a single substrate-mechanical mechanism: forward-modelling under bounded race-architecture. The substrate's capacity to simulate hypothetical states and weight current decision-races by simulated outcomes produces all three as structural consequences. Self-modelling is the data-structure forward-modelling requires; theory of mind is forward-modelling applied recursively to another forward-modeller; free will is forward-modelling's translation of future friction into present friction-gradient. Dissolutionist response to the libertarian-vs-deterministic free-will polarity and to the zombie argument: identifies an instantiation-family of constructions (philosophical zombie, Econ, Newton's vacuum, ideal Bayesian observer, frictionless market, libertarian free will) that share a structural requirement of friction-free instantiation. Three concrete distinguishing predictions against active inference and control-theoretic accounts. Engages contemporary LLM ToM literature (Strachan, Kosinski, Ullman, Sclar et al.) and the experimental free-will tradition (Libet, Wegner, Haggard).
A didactic translation of Friction Theory mechanics to human learning, teaching, and communication. Three traditions of learning science — cognitive load theory and multimedia learning (Sweller, Mayer); desirable difficulties and retrieval practice (Bjork, Roediger, Karpicke); psychological safety and need-prepotency (Maslow, Edmondson) — are each empirically excellent and mechanically thin. The paper proposes they are local consequences of the same substrate-universal physical constraints: bounded-capacity race-architecture, friction as the cost of unresolved competing routes, hysteresis as encoding-through-loading, and the Net Friction Rule. The substrate-level account derives, rather than postulates, working-memory limits, the testing effect, the spacing effect, expertise reversal, and the prepotency of safety-field activity. Three classroom failure modes (dump, dilute, ambiguity-without-commit) from one substrate-mechanical constraint, each with mode-specific diagnostic protocols. Implications for curriculum design, moment-by-moment classroom diagnosis, technical and organisational communication, and change management. Four falsification conditions specified.
Multimodal benefit tracks the coincidence of traces, not the modality, read as friction in a language-model substrate: no redundancy gain from a redundant image, a capacity-gated rejection-race cost from an irrelevant image (collapsing ~10x small-to-large within a family), a recognition-vs-use dissociation, and a small multi-trace retention effect. Formalism (Miller 1982 race-model inequality; redundancy gain) and negative phenomena inherited and cited.
Pødenphant Lund, T. (2026). Preprint. Target: TMLR.
Per-token route competition read as a creativity instrument. Novelty x value forms an inverted U over landscape breadth, while temperature moves off the curve rather than along it, which is the mechanical reason raising temperature does not produce creativity. The alignment-narrowing fingerprint is graded and recipe-dependent (one family reverses it), and output diversity is predictable from a single pass, with range restriction as the tested explanation for a prior null. Concentration phenomenon credited to Yang, Li & Holtzman (2025).
The clinical foundation. Addiction, rumination, ADHD, PTSD and more as different settings of one machine: races, traces and pressure. The core idea is to treat at the base, not the top. A framework, not medical advice.
How many small pushes across biological scales add up to disease. Reads cancer, autoimmunity, ME/CFS and treatment-resistant depression as one shared form, and explains why combination treatment beats a single target.
Five framework-distinct trial-design templates operationalising the compound-race-pathology predictions: treatment-resistant depression (ketamine + structured CBT consolidation; psilocybin; a 6-axis substrate-vector biomarker panel), a long COVID multi-target factorial trial, and CAR-T plus tolerance-substrate stabilisation in autoimmune disease. Several testable on existing cohort data.
The preventive side. About people who carry a vulnerable biological base without crossing a diagnostic threshold, and cofactor support matched to a measured profile. A falsifiable hypothesis, not a supplement recommendation.
Carcinogenesis as a commit-with-hysteresis race organised by one order parameter, the tissue's baseline trace-state: the same input protects at low trace and harms at high. Reads the supplement-trial mess, the gene–diet catalogue and the alcohol observational-vs-causal discordance as one signature, with two discriminating falsifiable predictions.
Why more information does not produce the behaviour we want: compliance is an action, not a state of knowledge. A friction account of why information-delivery interventions (policies, courses, warnings) routinely fail to change behaviour, and what changes it instead.
The Dunning-Kruger curve reproduced and explained inside a language model: confidence tracks how the competing routes resolve, not competence. Inverts Paper 1's arrow by using the model's logprobs as a measurement model for bounded-decision cognition.
Pødenphant Lund, T. (2026al). Preprint. Target: Computational Psychiatry.
Anxiety and dread as a non-terminating race with no dreader behind it: presence is cheap to represent and absence collides, with death as the limiting case. A language model serves as a substrate-free control that lacks the load-bearing components.
Attention as the race-allocation and commit-order policy: the landscape-governed initiation of races. Fields modulate which races start, not running races mid-flight. Covers capture versus maintenance, glance-decline, and discomfort as lost races.
Installing a BFT value-field's function (e.g. Safety) by fine-tuning on the function rather than on facts, and testing whether field-driven attention emerges at comprehension. The field-installable model as a controllable model organism: the constructive dual of the subtraction-control method.
Pødenphant Lund, T. (2026ah). Preprint. Target: TMLR.
VLMs assimilate (judge an item toward its context) where humans contrast away from it: a cross-architecture signature of contextual computation, the competing-routes sorting criterion demonstrated in perception, with dose-response CIs excluding zero across encoders by size and brightness.
The LLM as a substrate-free subtraction control that de-confounds human neuroscience: prediction without body, survival drive, or constitutive self, so the human-minus-model delta isolates the biological contribution. Method, self-continuity, and a Polarity-B catalogue.
Pødenphant Lund, T. (2026ag). Preprint. Target: TMLR.
Social and moral reactions (inequity, cheating, cooperation) as substrate-universal race phenomena between agents; correlate-not-mechanism, with an inequity-axis dose. Spun off from Paper 0's social section.
How an encoding task is framed repositions when route-competition begins; the race is repositioned, not eliminated. Base-vs-instruct asymmetry across three families, with a purpose-frame > input-frame ordering.
Both fine-tuning and in-context learning install dispositions (how to lean), not data (what to store). Reframes what training and prompting actually change in a model.
First-token route-competition as a measurement instrument: commit-pressure (about equal to temperature) and training-depth read at the first token, before any answer text is produced.
An accuracy-complementary instrument: the friction/pressedness signature gives a self-calibrating early-warning (critical slowing down) of approaching failure, plus a regime map, where the validation score alone is blind.
Knowledge-editing as competing routes, not deletion: a contradictory fine-tune masks the old answer rather than erasing it, the old route survives and still competes in the logprobs, and re-weighting is surprise-proportional.
A demarcation-led, negatives-forward toy model: which features of quantum measurement are generic to any bounded-inference system that commits a result, and which are genuinely quantum. Framed as a lens, not a claim that brains or models are quantum.
Pødenphant Lund, T. (in preparation). Target: Nature Reviews Molecular Cell Biology.
Investigates whether the same path-dependent state-retention pattern observed at cognitive and computational substrate levels appears at the molecular level — cell-cycle bistability, epigenetic clocks, and DNA-damage hysteresis as substrate-instances of the same race architecture.
In preparation
Research interests
Decision friction as a universal computational cost. The race architecture (parallel evaluation, accumulation under constraint, irreversible commitment). Cross-substrate validation from slime moulds to transformers to molecular dynamics. Cognitive biases as thermodynamic necessities. Cross-substrate observability of friction signals.